Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1405-75
Keywords
Normal-by-finite subgroup, CF-group, group of infinite rank
First Page
49
Last Page
53
Recommended Citation
GIOVANNI, F. D, & SACCOMANNO, F (2015). A note on infinite groups whose subgroups are close to be normal-by-finite. Turkish Journal of Mathematics 39 (1): 49-53. https://doi.org/10.3906/mat-1405-75
