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Spring/Summer 2003 Periodic groups with nearly modular subgroup lattice
M. De Falco, C. Musella, Y. P. Sysak, F. de Giovanni
Illinois J. Math. 47(1-2): 189-205 (Spring/Summer 2003). DOI: 10.1215/ijm/1258488147

Abstract

A theorem of B.H. Neumann states that each subgroup of a group $G$ has finite index in a normal subgroup of $G$ if and only if the commutator subgroup $G'$ of $G$ is finite, i.e., $G$ is finite-by-abelian. As a group lattice version of this theorem for a periodic group $G$, it is proved that each subgroup of $G$ has finite index in a modular subgroup of $G$ if and only if $G$ is an extension of a finite group by a group with modular subgroup lattice.

Citation

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M. De Falco. C. Musella. Y. P. Sysak. F. de Giovanni. "Periodic groups with nearly modular subgroup lattice." Illinois J. Math. 47 (1-2) 189 - 205, Spring/Summer 2003. https://doi.org/10.1215/ijm/1258488147

Information

Published: Spring/Summer 2003
First available in Project Euclid: 17 November 2009

zbMATH: 1032.20021
MathSciNet: MR2031315
Digital Object Identifier: 10.1215/ijm/1258488147

Subjects:
Primary: 20E15
Secondary: 20F50

Rights: Copyright © 2003 University of Illinois at Urbana-Champaign

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Vol.47 • No. 1-2 • Spring/Summer 2003
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