Groups with minimax commutator subgroup
A result of Dixon, Evans and Smith shows that if $G$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian, then $G$ itself has this property, i.e. the commutator subgroup of~$G$ has finite rank. It is proved here that if $G$ is a locally (soluble-by-finite) grou...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Isfahan
2014-03-01
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| Series: | International Journal of Group Theory |
| Subjects: | |
| Online Access: | http://www.theoryofgroups.ir/?_action=showPDF&article=2968&_ob=a0361dfd4b08b2933ad65f68ad95fcd2&fileName=full_text.pdf. |
| Summary: | A result of Dixon, Evans and Smith shows that if $G$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian, then $G$ itself has this property, i.e. the commutator subgroup of~$G$ has finite rank. It is proved here that if $G$ is a locally (soluble-by-finite) group whose proper subgroups have minimax commutator subgroup, then also the commutator subgroup $G'$ of $G$ is minimax. A corresponding result is proved for groups in which the commutator subgroup of every proper subgroup has finite torsion-free rank. |
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| ISSN: | 2251-7650 2251-7669 |