Semi-extraspecial Groups

Abstract

We survey the results regarding semi-extraspecial p-groups. Semiextraspecial 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.

On the minimal dimension of a faithful linear representation of a finite group

“…Any semiextraspecial group with center of the specified order also satisfies those hypotheses. As discussed in [23], these form a rather large family of groups. However, all of them have class 2.…”