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arXiv · 1709.03857

Semi-extraspecial Groups

Mark L. Lewis
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Abstract

We survey the results regarding semi-extraspecial $p$-groups. Semi-extraspecial groups can be viewed as generalizations of extraspecial groups. We present the connections between semi-extraspecial groups and Camina groups and VZ-groups, and give upper bounds on the order of the center and the orders of abelian normal subgroups. We define ultraspecial groups to be semi-extraspecial groups where the center is as large as possible, and demonstrate a connection between ultraspecial groups that have at least two abelian subgroups whose order is the maximum and semifields.

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Mark L. Lewis. 2017-09-12. Semi-extraspecial Groups. https://arxiv.org/abs/1709.03857

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