Stuttgart, Universiẗat, Diss., 1999.

Techn. Universiẗat, Diss., 2003--Berlin.

Thesis (Ph. D.)--Lehigh University, 2006. / Includes vita. Includes bibliographical references (leaves 191-197).

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In this dissertation we completely determine the maximal subgroups of the following finite simple groups: (i) POgX?) and 3D^q) for all prime powers q (ii) 2G2(32m+1) for all integers m (iii) G2(<7) for all odd prime powers q. Moreover, if Go is one of the groups appearing in (i), (ii) or (iii), then we also determine the maximal subgroups of all groups G satisfying: GO<G< Aut{Go\ (*) where Aut{Go) is the automorphism group of Go. Chapter 1 is devoted to the case Go = PClt(.q), where q = pt and p is prime. We first analyse the structure of the full automorphism group A = Aut(Go), as follows. Let Q be a quadratic form of Witt defect O defined on an 8-dimensional vector space V over F = GF(q). We write 0 = 0 (V,F£) for the isometry group of Q. We then define a chain of groups 0 <. SO < O < A < T all related to the geometry (V,¥,Q). The group T is the full semilinear group associated with Q and fl = [0,0] is a perfect group. Upon factoring out scalars, we obtain the projective groups PCI < PSO < PO < PA < PI\ We have Ptl = Go and | A:PT \ = 3. In fact, A is generated by Pr and a triality automorphism, which occurs because the Dynkin diagram of Go admits a symmetry of order 3. We then show that AlGo — Ex Z/, where E is the symmetric group S3 or S4. We thus obtain a homomorphism JT : A —» E whose kernel is isomorphic to GoXf. It turns out that G (as in (*)) contains a triality automorphism if and only if 3 divides | r(G)\. A recent theorem of M. Aschbacher [Invent, meth. 76 (1984), 469-514] shows that if G < PV, then the maximal subgroups of G fall into two families, which we may call C and S. Groups in C can be read off from from Aschbacher's paper, and we determine the groups in S by studying the p- modular representations of the finite simple groups. Thus we appeal to the classification of the finite simple groups. We then consider the case in which G •%. PY. Here G contains a triality automorphism and our argument goes roughly like this. Take Af to be a maximal subgroup of G which satisfies MGO = G and write M o = M n Go. Then M o < L < Go for some maximal subgroup L of Go. But M contains a triality automorphism T and so M o < L n U n Lr2. Now L is known because we have already handled the case in which G < PT (in particular, the case G = Go). Therefore our knowledge of L together with our knowledge concerning the action of r allows us to determine all possibilities for Mo. Hence M is known, for M £- MO.(G/GO). In Chapter 2 we treat the case Go = aD^(q). The group 3D4(<7) is the centralizer in PO^O?3) of a suitable triality automorphism. Thus the information about triauty which we collect in Chapter 1 is exploited in Chapter 2 to obtain the maximal subgroups of 3D^(q) and it automorphism groups. Similarly, G2O7) is the centralizer in PCl^iq) of a suitable triality. Thus in Chapter 3 we deal with the case Go = G2(?) (with q odd) by exploiting triality once again. Our methods for analysing G2O7) readily lend themselves to handle Go = 2Gi{q\ and this work is presented in Chapter 4. Chapter 4 also contains information about the maximal subgroups of the automorphism groups of the Suzuki groups Sz(q) = ^i^fa)- Note that in his original paper, Suzuki find the subgroups of the simple group We however find the maximal subgroups of all groups G satisfying < G < Aut(Sz(q)). In Chapter 5 we present lists of maximal subgroups of several families of low dimensional finite classical groups, including PSLn(q) for 2 < n < 11. We do not include proofs, although we sketch a proof for PSL&(q). Some of these results have appeared much earlier in the literature (dating as far back as the 19th century), but most of them are new.

A first order shear deformable finite strip with support displacements is introduced. Both nonlinear geometric effects and initial deflections may be considered. Support displacements are introduced by the use of a set of basis functions for support degrees of freedom. Each basis function is obtained by the solution of a Timoshenko beam under a unit displacement of the respective support degree of freedom. They are combined with the standard beam functions. The new finite strip can be applied to the analysis of rectangular containers and continuous plates with elastically restrained supports. The elastic restraints are introduced with independent springs acting along supports and nodal lines. The finite strip is extended to the analysis of unsymmetrically laminated clamped composite plates by the definition of equivalent elasticity modulii to find the basis functions. The new finite strip is used in the analysis of rectangular containers. It is shown that compressive horizontal forces exist in the walls of flexible containers filled with a liquid. This can only be predicted by the simultaneous consideration of the movement of the wall corners and the geometric nonlinearities, as can be done with the present model. A 'mode transition finite strip' which has unequal numbers of modes in the nodal lines is introduced. It can be used to economize the finite strip analysis of plates with loads that need a large number of modes, but spread only across a few of the strips. Also a study of the determination of transverse shear stresses by the use of the equilibrium equations and the displacement solution is made, resulting in some important and interesting observations. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate