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Enumerating isoclinism classes of semi-extraspecial groups

Published online by Cambridge University Press:  24 February 2020

Mark L. Lewis
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, OH44242, USA (lewis@math.kent.edu)
Joshua Maglione
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, D-33501Bielefeld, Germany (jmaglione@math.uni-bielefeld.de)

Abstract

We enumerate the number of isoclinism classes of semi-extraspecial p-groups with derived subgroup of order p2. To do this, we enumerate GL (2, p)-orbits of sets of irreducible, monic polynomials in 𝔽p[x]. Along the way, we also provide a new construction of an infinite family of semi-extraspecial groups as central quotients of Heisenberg groups over local algebras.

Type
Research Article
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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