- Turkish Journal of Mathematics
- Vol: 39 Issue: 1
- A note on infinite groups whose subgroups are close to be normal-by-finite
A note on infinite groups whose subgroups are close to be normal-by-finite
Authors : Francesco De Giovanni, Federica Saccomanno
Pages : 49-53
Doi:10.3906/mat-1405-75
View : 8 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Normal-by-finite subgroup, CF-group, group of infinite rank