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Criteria for Permutability to Be Transitive in Finite Groups

✍ Scribed by James C. Beidleman; Ben Brewster; Derek J.S. Robinson

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 113 KB
Volume: 222
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7964

No coin nor oath required. For personal study only.

✦ Synopsis

A group G is a PT -group if, for subgroups H and K with H permutable in K and K permutable in G, it is always the case that H is permutable in G. It is shown that a finite group is a soluble PT -group if and only if each subgroup of a Sylow subgroup is permutable in the Sylow normalizer.

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