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Hall Subgroups and π-Separable Groups

✍ Scribed by Zhaowei Du

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
173 KB
Volume
195
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let G be a finite group and a set of primes. In this paper, some new criteria for -separable groups and -solvable groups in terms of Hall subgroups are proved. The main results are the following:

Theorem. G is a -separable group if and only if Ž .

📜 SIMILAR VOLUMES

On π-Separable Groups
On π-Separable Groups
✍ Yakov Berkovich 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 173 KB

We generalize Lemmas 7.3᎐7.7 from the Odd Order paper. Those lemmas we extend from p-solvable groups to -separable groups, where is an arbitrary set Ä 4 of primes. Note that even in the case s p some of our results present proper Ž generalizations. In some proofs we use the solvability of groups of

Relative π-Blocks of π-Separable Groups,
Relative π-Blocks of π-Separable Groups, II
✍ A Laradji 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 109 KB

This correspondence allows us to prove results about relative -blocks by translating known results about -blocks. We continue to assume that N is a normal subgroup of G, but now we Ž . replace by any character in B N . In this paper, we extend the concept Ј Ž of relative -blocks to this general sit