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2014

Irredundant and minimal covers of finite groups

Lucchini, Andrea, Garonzi, Martino

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A cover of a finite non-cyclic group $G$ is a family $\mathcal{H}$ of proper subgroups of $G$ whose union equals $G$.

A cover of $G$ is called minimal if it has minimal size, and irredundant if it does not properly contain any other cover.
We classify the finite non-cyclic groups all of whose irredundant covers are minimal.

Irredundant and minimal covers of finite groups · Around

Built on

K. Doerk, T. Hawkes, Finite soluble groups. De Gruyter Expositions in Mathematics, 4. Walter de Gruyter & Co., Berlin, 1992
1992
Earlier work this paper cites.
D. J. S. Robinson, A course in the theory of groups; Second edition; Graduate Texts in Mathematics, 80. Springer-Verlag, New York, 1996
1996
Earlier work this paper cites.

Similar

M. J. Tomkinson, Groups as the union of proper subgroups; Math. Scand., 81(2) (1997), 191–198
1997
Cited alongside, same era.
R. A. Bryce, L. Serena, A note on minimal coverings of groups by subgroups. Special issue on group theory. J. Aust. Math. Soc. 71 (2001), no. 2, 159-168
2001
Cited alongside, same era.

Then

J. R. Rogério, A note on maximal coverings of groups. Comm. Algebra 42 (2014), no. 10, 4498-4508
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2014
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