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.
Normal-by-finite subgroup, CF-group, group of infinite rank
GIOVANNI, FRANCESCO DE and SACCOMANNO, FEDERICA
"A note on infinite groups whose subgroups are close to be normal-by-finite,"
Turkish Journal of Mathematics: Vol. 39:
1, Article 5.
Available at: https://journals.tubitak.gov.tr/math/vol39/iss1/5