Isomorphisms of group extensions

Group Homomorphisms and Isomorphisms

c W W L Chen, 1991, 1993, 2013. This chapter is available free to all individuals, on the understanding that it is not to be used for financial gain, and may be downloaded and/or photocopied, with or without permission from the author. However, this document may not be kept on any information storage and retrieval system without permission from the author, unless such system is not accessible t...

Natural Isomorphisms in Group Theory.

Extensions of isomorphisms for affine Grassmannians over F2

In Blok [1] affinely rigid classes of geometries were studied. These are classes B of geometries with the following property: Given any two geometries Γ1,Γ2 ∈ B with subspaces S1 and S2 respectively, then any isomorphism Γ1 −S1 −→ Γ2 −S2 uniquely extends to an isomorphism Γ1 −→ Γ2. Suppose Γ belongs to an affinely rigid class. Then it follows that for any subspace S we have Aut(Γ − S) ≤ Aut(Γ)....

Note on the Group of Isomorphisms*

LET SV a2, ••', sg represent all the operators of a group G and let tasa correspond to sa (a = 1, 2, •••, g) in any given simple isomorphism of G with itself. I t is evident that ta is some operator of G. When G is abelian these £a's must constitute a group T which is isomorphic with (?.* In this isomorphism, ta evidently can not be the inverse of sa unless sa = 1. As this condition is sufficie...

Isomorphisms of p-adic group rings

A long-standing problem, first posed by Graham Higman [15] and later by Brauer [4] is the “isomorphism problem for integral group rings.” Given finite groups G and H, is it true that ZG = ZH implies G 2: H? Many authors have worked on this question, but progress has been difficult [30]. Perhaps the best positive result was that of Whitcomb in 1968 [37], who showed that the implication G = H hol...