More on a question of M. Newman on isomorphic subgroups of solvable groups
Group Theory
2018-09-25 v1
Abstract
M.Newman has asked if it is the case that whenever H and K are isomorphic subgroups of a finite solvable group G with H maximal, then K is also maximal. This question was considered in a paper of I.M. Isaacs and the second author, where (among other things) the answer was shown to be affirmative if H has an Abelian Sylow 2-subgroup. Here, we show that the answer is affirmative unless the index of H is a power of a prime less than 5 and we obtain further restrictions on the structure of a purported minimal counterexample.
Cite
@article{arxiv.1809.08821,
title = {More on a question of M. Newman on isomorphic subgroups of solvable groups},
author = {George Glauberman and Geoffrey R. Robinson},
journal= {arXiv preprint arXiv:1809.08821},
year = {2018}
}