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Turkish Journal of Mathematics

DOI

10.3906/mat-1405-75

Abstract

A group G is said to have the CF-property if the index X:X_G is finite for every subgroup X of G. Extending previous results by Buckley, Lennox, Neumann, Smith, and Wiegold, it is proven here that if G is a locally graded group whose proper subgroups have the CF-property, then G is abelian-by-finite, provided that all its periodic sections are locally finite. Groups in which all proper subgroups of infinite rank have the CF-property are also studied.

First Page

49

Last Page

53

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