Factorization of group homomorphisms

Lattice Homomorphisms Induced by Group Homomorphisms

Introduction. By a lattice homorphism of a group G onto a group G' we mean a single-valued mapping of the lattice L(G) of subgroups of G onto the lattice L(G') of subgroups of G', which preserves all unions and intersections, that is, which is subject to the conditions 1. (U,S,)0 = U,(S¿), 2. (r\vSr) = Ç)ASd>), for every (finite or infinite) set of subgroups 5„ of G. We call proper any l...

Computing with Group Homomorphisms

Let G = (X) and H be finite groups and let r : X ~ H be a map from the generating set X of G into H. We describe a simple approach for deciding whether or not r determines a group homomorphism from G to H, and if it does, for computing the kernel of r If O and H are permutation groups the algorithm is a simple application of standard algorithms for bases and strong generating sets. If G and H a...

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...

Automatic continuity of group homomorphisms

We survey various aspects of the problem of automatic continuity of homomorphisms between Polish groups.

Norm Decreasing Homomorphisms of Group Algebras