Subnormal joins and subgroups of finite index

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1984 English Publisher:Springer Science and Business Media LLCJournal:Archiv der Mathematik, volume 43, pages 481-482 (issn: 0003-889X, eissn: 1420-8938,

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Authors: Smith, Howard;

doi: 10.1007/bf01190947

Subnormal joins and subgroups of finite index

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Abstract

The following theorem is proved: Suppose \(G=\), where H, K are subnormal in G, and let A, B be such that H/A and K/B are finite \(\pi\)- groups. If G' has finite abelian section rank, then \(J=\) has finite \(\pi\)-index in G. In particular, J is subnormal.

Related Organizations

University of Würzburg
Germany

Keywords

subgroups of finite index, joins of subnormal subgroups, finite abelian section rank, Chains and lattices of subgroups, subnormal subgroups, Subgroup theorems; subgroup growth

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