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arXiv · 1603.08184

Permutation-like Matrix Groups with a Maximal Cycle of Length Power of Two

Guodong Deng·Yun Fan
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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.

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Guodong Deng, Yun Fan. 2016-03-27. Permutation-like Matrix Groups with a Maximal Cycle of Length Power of Two. https://arxiv.org/abs/1603.08184

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