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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. …
Groups Of Divisibility, Seth J. Gerberding
Groups Of Divisibility, Seth J. Gerberding
Honors Thesis
In this thesis, we examine a part of abstract algebra known as Groups of Divisibility. We construct these special groups from basic concepts. We begin with partially-ordered sets, then build our way into groups, rings, and even structures akin to rings of polynomials. In particular, we explore how elementary algebra evolves when an ordering is included with the operations. Our results follow the work done by Anderson and Feil, however we include more explicit proofs and constructions. Our primary results include proving that a group of divisibility can be provided with an order to make it a partially-ordered group; that …