On the primary coverings of finite solvable and symmetric groups-Reference-Cited by-同舟云学术

On the primary coverings of finite solvable and symmetric groups

Published:2021-07-01 Issue:6 Volume:24 Page:1189-1211
ISSN:1433-5883
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Fumagalli Francesco¹,Garonzi Martino²

Affiliation:

1. Dipartimento di Matematica e Informatica “Ulisse Dini” , Università degli Studi di Firenze , viale Morgagni 67/A, 50134 Firenze , Italy

2. Departamento de Matemática , Universidade de Brasília , Campus Universitário Darcy Ribeiro , Brasília – DF 70910-900 , Brazil

Abstract

Abstract A primary covering of a finite group 𝐺 is a family of proper subgroups of 𝐺 whose union contains the set of elements of 𝐺 having order a prime power. We denote by σ 0 ⁢ ( G )

\sigma_{0}(G)

the smallest size of a primary covering of 𝐺 and call it the primary covering number of 𝐺. We study this number and compare it with its analogue σ ⁢ ( G )

\sigma(G)

, the covering number, for the classes of groups 𝐺 that are solvable and symmetric.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/jgth-2020-0056/pdf

Reference17 articles.

1. J. H. E. Cohn, On 𝑛-sum groups, Math. Scand. 75 (1944), 44–58.

2. J. D. Dixon and B. Mortimer, Permutation Groups, Grad. Texts in Math. 163, Springer, New York, 1996.

3. B. Fein, W. M. Kantor and M. Schacher, Relative Brauer groups. II, J. Reine Angew. Math. 328 (1981), 39–57.

4. F. Fumagalli, On the indices of maximal subgroups and the normal primary coverings of finite groups, J. Group Theory 22 (2019), no. 6, 1015–1034.

5. W. Gaschütz, Die Eulersche Funktion endlicher auflösbarer Gruppen, Illinois J. Math. 3 (1959), 469–476.