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On the primary coverings of finite solvable and symmetric groups

  • Francesco Fumagalli and Martino Garonzi EMAIL logo
From the journal Journal of Group Theory

Abstract

A primary covering of a finite group ๐บ is a family of proper subgroups of ๐บ whose union contains the set of elements of ๐บ having order a prime power. We denote by ฯƒ 0 โข ( G ) the smallest size of a primary covering of ๐บ and call it the primary covering number of ๐บ. We study this number and compare it with its analogue ฯƒ โข ( G ) , the covering number, for the classes of groups ๐บ that are solvable and symmetric.

Award Identifier / Grant number: 03/2016

Award Identifier / Grant number: 302134/2018-2

Award Identifier / Grant number: 422202/2018-5

Funding statement: M. Garonzi was supported by Fundaรงรฃo de Apoio ร  Pesquisa do Distrito Federal (FAPDF) โ€“ demanda espontรขnea 03/2016, and by Conselho Nacional de Desenvolvimento Cientรญfico e Tecnolรณgico (CNPq) โ€“ Grant numbers 302134/2018-2, 422202/2018-5.

Acknowledgements

The authors are grateful to the referee for the careful reading of the paper and for completing the calculations of ฯƒ 0 โข ( S 10 ) using [16, 17].

  1. Communicated by: Evgeny Vdovin

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Received: 2020-04-13
Revised: 2021-04-15
Published Online: 2021-07-01
Published in Print: 2021-11-01

ยฉ 2021 Walter de Gruyter GmbH, Berlin/Boston

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