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 : 9 | Download : 6

Publication Date : 0000-00-00

Article Type : Research Paper

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