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.
Keywords
Normal-by-finite subgroup, CF-group, group of infinite rank
First Page
49
Last Page
53
Recommended Citation
GIOVANNI, FRANCESCO DE and SACCOMANNO, FEDERICA
(2015)
"A note on infinite groups whose subgroups are close to be normal-by-finite,"
Turkish Journal of Mathematics: Vol. 39:
No.
1, Article 5.
https://doi.org/10.3906/mat-1405-75
Available at:
https://journals.tubitak.gov.tr/math/vol39/iss1/5
