Enumerating isoclinism classes of semi-extraspecial groups

Mark L. Lewis; Joshua Maglione

doi:10.1017/S0013091519000531

Enumerating isoclinism classes of semi-extraspecial groups

Mark L. Lewis
, Joshua Maglione

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

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 p[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.

Original language	English
Pages (from-to)	426-442
Number of pages	17
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	63
Issue number	2
DOIs	https://doi.org/10.1017/S0013091519000531
Publication status	Published - 1 May 2020
Externally published	Yes

Keywords

Pfaffian
bilinear maps
genus 2

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10.1017/S0013091519000531

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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 p[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.",

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AB - 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 p[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.

KW - Pfaffian

KW - bilinear maps

KW - genus 2

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Enumerating isoclinism classes of semi-extraspecial groups

Abstract

Keywords

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