15,218 research outputs found
On the Prime Graph Question for Integral Group Rings of 4-primary groups I
We study the Prime Graph Question for integral group rings. This question can
be reduced to almost simple groups by a result of Kimmerle and Konovalov. We
prove that the Prime Graph Question has an affirmative answer for all almost
simple groups having a socle isomorphic to for , establishing the Prime Graph Question for the first time for all
automorphic extensions of series of simple groups. Using this, we determine
exactly how far the so-called HeLP-method can take us for (almost simple)
groups having an order divisible by at most different primes.Comment: [v3] 32 pages. Final versio
A Homological Approach to Factorization
Mott noted a one-to-one correspondence between saturated multiplicatively
closed subsets of a domain D and directed convex subgroups of the group of
divisibility D. With this, we construct a functor between inclusions into
saturated localizations of D and projections onto partially ordered quotient
groups of G(D). We use this functor to construct many cochain complexes of
o-homomorphisms of po-groups. These complexes naturally lead to some
fundamental structure theorems and some natural homology theory that provide
insight into the factorization behavior of D.Comment: Submitted for publication 12/15/201
- …