Enumerating isoclinism classes of semi-extraspecial groups. Issue 2 (24th May 2020)

• Record Type: Journal Article
• Authors: Lewis, Mark L.; Maglione, Joshua
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 63:Issue 2(2020)
• Page Start: 426
• Page End: 442
• Publication Date: 2020-05-24
• Subjects: Pfaffian, -- genus 2, -- bilinear maps; 20D15, -- 20D60; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091519000531
• Languages: English
• ISSNs: 0013-0915

Abstract

Abstract: We enumerate the number of isoclinism classes of semi-extraspecial p -groups with derived subgroup of order p 2 . To do this, we enumerate GL (2, p )-orbits of sets of irreducible, monic polynomials in 𝔽 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.