On ramification structures for finite nilpotent groups

Year 2019, Volume: 48 Issue: 6, 1642 - 1652, 08.12.2019

Şükran Gül

Abstract

We extend the characterization of abelian groups with ramification structures given by Garion and Penegini in [Beauville surfaces, moduli spaces and finite groups, Comm. Algebra, 2014] to finite nilpotent groups whose Sylow $p$-subgroups have a `nice power structure', including regular $p$-groups, powerful $p$-groups and (generalized) $p$-central $p$-groups. We also correct two errors in [Beauville surfaces, moduli spaces and finite groups, Comm. Algebra, 2014] regarding abelian $2$-groups with ramification structures and the relation between the sizes of ramification structures for an abelian group and those for its Sylow $2$-subgroup.

Keywords

ramification structures, Beauville structures, finite nilpotent groups, finite $p$-groups

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