Semi-extraspecial Groups

2017/09/12 by Lewis, Mark L. · 1 citation
#20D15 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1709.03857

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.

Cited by

• Finite groups of non-prime-power order with exactly four character codegrees

Related

• Semi-extraspecial groups with an abelian subgroup of maximal possible order
• Semi-extraspecial p-groups with automorphisms of large order
• Element orders in extraspecial groups
• Set-theoretic aspects of periodic FC-groups --- extraspecial p-groups and Kurepa trees
• Semi-p-abelian group