Finite coverings by normal subgroups

Brodie, M. A.; Chamberlain, R. F.; Kappe, L.-C.

doi:10.1090/S0002-9939-1988-0964841-9

Finite coverings by normal subgroups
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by M. A. Brodie, R. F. Chamberlain and L.-C. Kappe PDF

Proc. Amer. Math. Soc. 104 (1988), 669-674 Request permission

Abstract:

B. H. Neumann’s characterization of groups possessing a finite covering by proper subgroups and Baer’s characterization of groups with finite coverings by abelian subgroups are refined to results about finite coverings by normal subgroups. Various corollaries about the structure of groups having such finite coverings are derived. Using the method employed for the main theorem, a simplified proof of an earlier result of the third author concerning finite coverings by word subgroups is given.

References

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Invariantly covered groups

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Finiteness conditions and generalized soluble groups