On ramification structures for finite nilpotent groups

Authors : Şükran GÜL

Pages : 1642-1652

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Publication Date : 2019-12-08

Article Type : Research Paper

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 insert ignore into journalissuearticles values(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