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Full-Text Articles in Algebra
On The Local Theory Of Profinite Groups, Mohammad Shatnawi
On The Local Theory Of Profinite Groups, Mohammad Shatnawi
Dissertations
Let G be a finite group, and H be a subgroup of G. The transfer homomorphism emerges from the natural action of G on the cosets of H. The transfer was first introduced by Schur in 1902 [22] as a construction in group theory, which produce a homomorphism from a finite group G into H/H' an abelian group where H is a subgroup of G and H' is the derived group of H. One important first application is Burnside’s normal p-complement theorem [5] in 1911, although he did not use the transfer homomorphism explicitly to prove it. …
Resolving Classes And Resolvable Spaces In Rational Homotopy Theory, Timothy L. Clark
Resolving Classes And Resolvable Spaces In Rational Homotopy Theory, Timothy L. Clark
Dissertations
A class of topological spaces is called a resolving class if it is closed under weak equivalences and homotopy limits. Letting R(A) denote the smallest resolving class containing a space A, we say X is A-resolvable if X is in R(A), which induces a partial order on spaces. These concepts are dual to the well-studied notions of closed class and cellular space, where the induced partial order is known as the Dror Farjoun Cellular Lattice. Progress has been made toward illuminating the structure of the Cellular Lattice. For example: Chachólski, Parent, and Stanley have shown that it …