On ramification structures for finite nilpotent groups
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.
___
- [1] N. Boston, A survey of Beauville p-groups,in: Beauville Surfaces and Groups, editors I. Bauer, S. Garion, A. Vdovina, Springer Proceedings in Mathematics & Statistics, 123, 35–40, Springer, 2015.
- [2] B. Fairbairn, Recent work on Beauville surfaces, structures and groups, in: Groups St Andrews 2013, editors C.M. Campbell, M.R. Quick, E.F. Robertson and C.M. Roney- Dougal, London Mathematical Society Lecture Note Series, 422, 225–241, 2015.
- [3] G.A. Fernández-Alcober, Omega subgroups of powerful p-groups, Israel J. Math. 162, 75–79, 2007.
- [4] G.A. Fernández-Alcober and Ş. Gül, Beauville structures in finite p-groups, J. Algebra, 474, 1–23, 2017.
- [5] S. Garion and M. Penegini, New Beauville surfaces and finite simple groups, Manuscripta Math. 142, 391–408, 2013.
- [6] S. Garion and M. Penegini, Beauville surfaces, moduli spaces and finite groups, Comm. Algebra, 42, 2126–2155, 2014.
- [7] G. Jones, Beauville surfaces and groups: a survey, in: Rigidity and Symmetry, editors R. Connelly, A.I. Weiss, W. Whiteley, Fields Institute Communications, 70, Springer, 205–225, 2014.
- [8] L. Ribes and P. Zalesskii, Profinite Groups, second edition, Springer, 2010.
- [9] D.J.S. Robinson, A Course in the Theory of Groups, second edition, Springer, 1996.
- [10] M. Suzuki, Group Theory II, Springer, 1986.
- [11] M. Xu, A class of semi-p-abelian p-groups, Kexue Tongbao, 27, 142–146, 1982.
- Yayın Aralığı: 6
- Başlangıç: 2002
- Yayıncı: Hacettepe Üniversitesi Fen Fakultesi