The Lyons group denoted by Ly is a Sporadic Simple Group of order 51765179004000000 = 28 37 56 7 11 31 37 67. It(Ly) has a trivial Schur Multiplier and a trivial Outer Automorphism Group. Its maximal subgroups are G2(5) of order 5859000000 and index 8835156, 3 McL:2 of order 5388768000 and index 9606125, 53 L3(5) of order 46500000 and index 1113229656, 2 A11 of order 29916800 and index 1296826875, 51+4 + :4S6 of order 9000000 and index 5751686556, 35:(2 M11) of order 3849120 and index 13448575000, 32+4:2 A5 D8 of order 699840 and index 73967162500, 67:22 of order 1474 and index 35118846000000 and 37:18 of order 666 and index 77725494000000. Its existence was suggested by Richard Lyons. Lyons characterized its order as the unique possible order of any nite simple group where the centralizer of some involution is isomorphic to the nontrivial central extension of the alternating group of degree 11 by the cyclic group of order 2. Sims proved the existence of this group and its uniqueness using permutations and machine calculations. In this dissertation, we compute the (p; q; t)-generations of the Lyons group for dis- tinct primes p, q and t which divide the order of Ly such that p < q < t. For computations, we made use of the Computer Algebra System GAP / Mathematical Sciences / M.Sc. (Mathematics)

Une partie symétrique X d'un groupe G est un sous-groupe K-approximatif s'il existe une partie finie E ⊂ G de taille K telle que X2 ⊂ E.X. L'étude combinatoire des groupes approximatifs a grandement bénéficié des apports de la Théorie des Modèles : en 2009, Hrushovski montre qu'une ultralimite de groupes approximatifs finis possède une composante connexe modèle-théorique, donc un quotient localement compact X/H. En appliquant les résultats de Gleason et Yamabe sur le cinquième problème de Hilbert, cela permet de trouver un morphisme vers un groupe de Lie, et d'en déduire des résultats de nilpotence. Cela a permis à Breuillard, Green et Tao de classifier tous les groupes approximatifs finis, en retrouvant un quotient X/H de manière combinatoire. Dans cette thèse, on s'intéresse à la construction d'un sous-groupe H type-définissable et d'indice borné, qui garantit l'existence d'un quotient localement compact. On montre que l'approche combinatoire de Breuillard, Green et Tao peut être vue de cette manière, et on la généralise à tous les groupes approximatifs définissablement moyennables. On montre aussi que si H est type-définissable dans un langage L∗, alors on peut construire un sous-groupe H qui est type-définissable sur un langage réduit L, et toujours d'indice borné. L'existence de H ne dépend donc pas du choix du langage / A symmetric subset X in a group G is a K-approximate subgroup if there exists a finite set E ⊂ G of cardinality K such that X2 ⊂ E.X. The study of approximate subgroups in multiplicative combinatorics experienced a significate advance through the use of model theory. In 2009, Hrushovski showed that an ultralimit of finite approximate subgroups has a model-theoretic connected component, thus a locally compact quotient X/H. Using the results of Gleason and Yamabe about Hilbert’s fifth problem, this allows the construction of a morphism to a Lie group, and deduce some results about nilpotency. This lead to the theorem of Breuillard, Green and Tao classifying all finite approximate subgroups, using a combinatorial construction of the quotient X/H. In this thesis, we are intersested in the conditions needed to construct a type definable subgroup H of bounded index in X. This implies the existence of a locally compact quotient.We show that the combinatorial construction of Breuillard, Green and Tao can be seen in a definable way, and give a generalisation to all definably amenable approximate subgroups. Also, we show that if H is type-definable in a language L∗, then it is possible to construct a subgroup H which is type-definable in a reduct L, still with bounded index. Thus the existence of a subgroup H does not depend on the choice of a base language.

The Lyons group denoted by Ly is a Sporadic Simple Group of order 51765179004000000 = 28 37 56 7 11 31 37 67. It(Ly) has a trivial Schur Multiplier and a trivial Outer Automorphism Group. Its maximal subgroups are G2(5) of order 5859000000 and index 8835156, 3 McL:2 of order 5388768000 and index 9606125, 53 L3(5) of order 46500000 and index 1113229656, 2 A11 of order 29916800 and index 1296826875, 51+4 + :4S6 of order 9000000 and index 5751686556, 35:(2 M11) of order 3849120 and index 13448575000, 32+4:2 A5 D8 of order 699840 and index 73967162500, 67:22 of order 1474 and index 35118846000000 and 37:18 of order 666 and index 77725494000000. Its existence was suggested by Richard Lyons. Lyons characterized its order as the unique possible order of any nite simple group where the centralizer of some involution is isomorphic to the nontrivial central extension of the alternating group of degree 11 by the cyclic group of order 2. Sims proved the existence of this group and its uniqueness using permutations and machine calculations. In this dissertation, we compute the (p; q; t)-generations of the Lyons group for dis- tinct primes p, q and t which divide the order of Ly such that p < q < t. For computations, we made use of the Computer Algebra System GAP / Mathematical Sciences / M.Sc. (Mathematics)

No description available.

The purpose of this dissertation was to study how teachers and school leaders perceived a specific set of classroom math innovations, and how those innovations impacted instruction in relation to the Georgia Vision Project (GVP) standards and recommendations. This was a qualitative study conducted in two GVP districts. The participants in the study were five elementary teachers, two school administrators, and two district leaders. The participants were interviewed to gain an understanding of their perceptions of recent math innovations. The innovations included (a) math instruction using manipulatives (such as counting objects and puzzles) that utilize the Concrete Representational Abstract (CRA) model, which engages students to conceive from the concrete to the abstract; (b) differentiation through flexible student grouping; (c) information about how different subgroups of students learn mathematics; and (d) math professional learning. Previous research had focused on these innovations separately. However, no research study had grouped these innovations together to see how teachers perceived them within the context of a math classroom, and how teachers implemented them in their classrooms in order to increase student achievement. This qualitative case study included schoolteacher and educational leader interviews, observations, and artifacts. The two districts in the study were high performing in the area of mathematics. The results indicated that schoolteachers and educational leaders could not directly relate the math innovations to student success and, moreover, to the GVP standards and recommendations. During the study all GVP standards were analyzed at varying levels. The study primarily focused on the teaching and learning standard, which was a significant initiative for both districts. Both districts had varying levels of implementation concerning the innovations in the study: (a) use of manipulatives, (b) differentiation in classrooms, and (c) professional learning. All participants referenced the innovations as a part of their instruction, but could not directly relate the innovations beneficial to the success of the students.

The main result of this thesis is an original proof that every word has finite width in a compact $p$-adic analytic group. The proof we give here is an alternative to Andrei Jaikin-Zapirain's recent proof of the same result, and utilises entirely group-theoretical ideas. We accomplish this by reducing the problem to a proof that every word has finite width in a profinite group which is virtually a polycyclic pro-$p$ group. To obtain this latter result we first establish that such a group can be embedded as an open subgroup of a group of the form $N_1M_1$, where $N_1$ is a finitely generated closed normal nilpotent subgroup, and $M_1$ is a finitely generated closed nilpotent-by-finite subgroup; we then adapt a method of V. A. Romankov. As a corollary we note that our approach also proves that every word has finite width in a polycyclic-by-finite group (which is not profinite). As a supplementary result we show that for finitely generated closed subgroups $H$ and $K$ of a profinite group the commutator subgroup $[H,K]$ is closed, and give examples to show that various hypotheses are necessary. This implies that the outer-commutator words have finite width in profinite groups of finite rank. We go on to establish some bounds for this width. In addition, we show that every word has finite width in a product of a nilpotent group of finite rank and a virtually nilpotent group of finite rank. We consider the possible application of this to soluble minimax groups.

Denna tvärsnittsstudie syftade till att undersöka samförekomst av smärtrelaterad rädsla och social ångest i ett kliniskt sample med kronisk smärtproblematik. Syftet var också att beskriva och kontrastera samvariation av transdiagnostiska faktorer i eventuella subgrupper. Datan bestod av enkätsvar från 196 deltagare i Social ångest smärta-projektet som leds av Örebro universitet och Akademiska sjukhuset i Uppsala. En klusteranalys fick fram fyra subgrupper bland deltagarna. En subgrupp utmärkte sig för hög komorbiditet. Denna grupp visade höga nivåer av tänkbara transdiagnostiska faktorer som ångestkänslighet och negativ affekt, samt hög smärtkatastrofiering. Det diskuterades kring dessa faktorers roll som sårbarhets- och vidmakthållandeprocesser, utifrån aktuella teoretiska modeller. Studiens kliniska implikationer belyser behovet av hänsyn till dessa faktorers roll vid behandling och framtida forskning. / This cross-sectional study aimed to explore co-occurrence of pain-related fear and social anxiety in a clinical sample with chronic pain. The purpose was also to describe and contrast co-variation of transdiagnostic factors in potential subgroups. The data consisted of 196 answered questionnaires from the Social anxiety pain-project led by Örebro University and the Uppsala University Hospital. A cluster analysis produced four subgroups among the participants. One subgroup was salient for its high comorbidity. This group showed high levels of potential transdiagnostic factors such as anxiety sensitivity and negative affect, as well as high pain catastrophizing. These factors are discussed in terms of their role as vulnerability and maintaining factors, in the light of current theoretical models. The clinical implications of this study suggest taking the role of these factors into account in aspects of treatment and future research.

No description available.

One might easily argue that the Classification of Finite Simple Groups is one of the most important theorems of group theory. Given that any finite group can be deconstructed into its simple composition factors, it is of great importance to have a detailed knowledge of the structure of finite simple groups. One of the classes of finite groups that appear in the classification theorem are the simple classical groups, which are matrix groups preserving some form. This thesis will shed some new light on almost simple classical groups in dimension 13, 14 and 15. In particular we will determine their maximal subgroups. We will build on the results by Bray, Holt, and Roney-Dougal who calculated the maximal subgroups of all almost simple finite classical groups in dimension less than 12. Furthermore, Aschbacher proved that the maximal subgroups of almost simple classical groups lie in nine classes. The maximal subgroups in the first eight classes, i.e. the subgroups of geometric type, were determined by Kleidman and Liebeck for dimension greater than 13. Therefore this thesis concentrates on the ninth class of Aschbacher's Theorem. This class roughly consists of subgroups which are almost simple modulo scalars and do not preserve a geometric structure. As our final result we will give tables containing all maximal subgroups of almost simple classical groups in dimension 13, 14 and 15.

<p>Although subgroups are a central component of work teams, they have remained largely unexamined by organizational scholars. In three chapters, a theory and measure of subgroups are developed and then tested. The theory introduces a typology of subgroups and a depiction of the antecedents and consequences of subgroups. The measure, called the subgroup algorithm, determines the most dominant configurations of subgroups in real work teams--those that are most likely to influence team processes and outcomes. It contrasts the characteristics within a subgroup or set of subgroups versus the characteristics between subgroups or a set of subgroups for every potential configuration of subgroups on every work team in a given sample. The algorithm is tested with a simulation, with results suggesting that it adds value to the methodological literature on subgroups. The empirical test uses the subgroup algorithm to test key propositions put forth in the theory of subgroups. First, it is predicted that teams will perform better when identity-based subgroups are unequal in size and knowledge-based subgroups are equal in size. Second, it is predicted that, although teams will perform better with an increasing number of both identity-based and knowledge-based subgroups, there will be a discontinuity in this linear function for identity-based subgroups: teams with two identity-based subgroups will perform more poorly than teams with any other number of identity-based subgroups. The subgroup algorithm is used to test these predictions in a sample of 326 work teams. Results generally support the predictions.</p> / Dissertation