Group factorisations, uniform automorphisms, and permutation groups of simple diagonal type
Group Theory
2017-06-01 v2
Abstract
We present a new proof, which is independent of the finite simple group classification and applies also to infinite groups, that quasiprimitive permutation groups of simple diagonal type cannot be embedded into wreath products in product action. The proof uses several deep results that concern factorisations of direct products involving subdirect subgroups. We find that such factorisations are controlled by the existence of uniform automorphisms.
Cite
@article{arxiv.1611.01103,
title = {Group factorisations, uniform automorphisms, and permutation groups of simple diagonal type},
author = {Cheryl E. Praeger and Csaba Schneider},
journal= {arXiv preprint arXiv:1611.01103},
year = {2017}
}
Comments
16 pages