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Semi-extraspecial Groups

  • Mark L. LewisEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 277)

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, 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.

Keywords

p-group Extraspecial group Semifields 

Mathematics Subject Classification 2010:

20D15 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesKent State UniversityKentUSA

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