A note on infinite groups whose subgroups are close to be normal-by-finite | Zendy

Francesco de Giovanni | Zendy; Federica Saccomanno | Zendy

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A note on infinite groups whose subgroups are close to be normal-by-finite

Author(s) -

Francesco de Giovanni,

Federica Saccomanno

Publication year - 2015

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1405-75

Subject(s) - mathematics , property (philosophy) , abelian group , locally finite group , group (periodic table) , normal subgroup , von neumann architecture , rank (graph theory) , combinatorics , pure mathematics , physics , quantum mechanics , philosophy , epistemology

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.

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