Dergiler / Turkish Journal of Mathematics / 2015 / Cilt: 39 - Sayı: 1
A note on infinite groups whose subgroups are close to be normal-by-finite
- Sayfa
- 49–53
- DOI
- —
Özet
A group G is said to have the CF-property if the index |X:XG| 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.
Abstract
A group G is said to have the CF-property if the index |X:XG| 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.