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G. Cutolo, E.I. Khukhro, J.C. Lennox, S. Rinauro, H. Smith and J. Wiegold
Locally finite groups all of whose subgroups are boundedly finite over their cores
Bull. London Math. Soc., 29, (1997), pp. 563–570.
doi: 10.1112/s0024609397003068
MathSciNet Zentralblatt Comments Abstract Full Text
Abstract
For n a positive integer, a group G is called core-n if H/HG has order at most n for every subgroup H of G (where HG is the normal core of H, the largest normal subgroup of G contained in H). It is proved that a locally finite core-n group G has an abelian subgroup whose index in G is bounded in terms of n.
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