We prove two theorems concerning the action of the Steenrod algebra in cohomology and homology. (i) Let A denote a finitely generated graded F_p polynomial algebra over the Steenrod algebra whose generators have dimensions not divisible by p. The possible sets of dimensions of the generators for such A are known. It was conjectured that if we replaced the polynomial algebra A by a polynomial algebra truncated at some height greater than p over the Steenrod algebras, the sets of all possible dimensions would coincide with the former list. We show that the conjecture is false. For example F₁₁[x₆,x₁₀]¹² truncated at height 12 supports an action of the Steenrod algebra but F₁₁[x₆,x₁₀] does not. (ii) Let V be an elementary abelian 2-group of rank 3. The problem of determining a minimal set of generators for H*(BV,F₂) over the Steenrod algebra was an unresolved problem for many years. (A solution was announced by Kameko in June 1990, but is not yet published.) A dual problem is to determine the subring M of the Pontrjagin ring H*(BV,F₂). We determine this ring completely and in particular give a verification that the minimum number of generators needed in each dimension in cohomology is as announced by Kameko, but by using completely different techniques. Let v ε V - (0) and denote by a_5(v) ε H*(BV,F₂) the image of the non-zero class in H_2s-1(RP^∞,F₂) imeq F₂ under the homomorphism induced by the inclusion of F_{2 → V onto (0,v). We show that M is isomorphic to the ring generated by (a}_s(v),s ≥ 1, v ε V - (0)) except in dimensions of the form 2^r+3 + 2^r+1 + 2^r - 3, r ≥ 0, where we need to adjoin our additional generator.

Thesis (M.S.)--Oregon State College, 1952. / Typescript. Includes bibliographical references (leaf 21). Also available on the World Wide Web.

Thesis (Ph. D.)--University of Oregon, 2007. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 80-83) and index. Also available for download via the World Wide Web; free to University of Oregon users.

Thesis (Ph. D.)--McMaster University (Canada), 1996. / Source: Dissertation Abstracts International, Volume: 58-06, Section: B, page: 3083. Adviser: V.P. Snaith.

Thesis (M.A. 1971) from the Department of Mathematics, University of Adelaide.

Thesis (Ph. D.)--Northeastern University, 2008. / Title from title page (viewed March 26, 2009). Graduate School of Arts and Sciences, Dept. of Mathematics. Includes bibliographical references (p.80-82).

Thesis (B.S.)--University of Missouri, School of Mines and Metallurgy, 1882. / The entire thesis text is included in file. Holograph [Handwritten and illustrated in entirety by author]. Title from title screen of thesis/dissertation PDF file (viewed January 6, 2009)

Thesis (Ph. D.)--Catholic University of America, 1942. / Reproduced from type-written copy.

Thesis (Ph. D.)--West Virginia University, 2008. / Title from document title page. Document formatted into pages; contains iv, 45 p. : ill. Includes abstract. Includes bibliographical references (p. 45).

Thesis--Dartmouth College, 1966. / Bibliography: leaf 36.