Permutation-like Matrix Groups with a Maximal Cycle of Length Power of Two
Group Theory
2016-03-29 v1
Abstract
If every element of a matrix group is similar to a permutation matrix, then it is called a permutation-like matrix group. References [4], [5] and [6] showed that, if a permutation-like matrix group contains a maximal cycle such that the maximal cycle generates a normal subgroup and the length of the maximal cycle equals to a prime, or a square of a prime, or a power of an odd prime, then the permutation-like matrix group is similar to a permutation matrix group. In this paper, we prove that if a permutation-like matrix group contains a maximal cycle such that the maximal cycle generates a normal subgroup and the length of the maximal cycle equals to any power of 2, then it is similar to a permutation matrix group.
Keywords
Cite
@article{arxiv.1603.08184,
title = {Permutation-like Matrix Groups with a Maximal Cycle of Length Power of Two},
author = {Guodong Deng and Yun Fan},
journal= {arXiv preprint arXiv:1603.08184},
year = {2016}
}