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This article is cited in 1 scientific paper (total in 1 paper)
Some criteria for the decomposability of finite groups
V. M. Busarkin, N. D. Podufalov Krasnoyarsk State University
Abstract:
In this paper we prove the following fundamental results.
\underline{Theorem 1}: A finite unsolvable group, every involution of which is contained
in a proper isolated subgroup, is decomposable.
\underline{Theorem 2}: Suppose the finite unsolvable group $G$ contains a strongly
isolated subgroup $M$ of odd order with isolated normalizer $N(M)$ of even order.
If $|N(M):(M)|>2$, the group $G$ is isomorphic with one of the groups: 1) $PSL(2,q)$, $q$ odd; 2) $PGL(2,q)$, $q$ odd.
Received: 03.06.1971
Citation:
V. M. Busarkin, N. D. Podufalov, “Some criteria for the decomposability of finite groups”, Mat. Zametki, 12:6 (1972), 717–725; Math. Notes, 12:6 (1972), 871–875
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https://www.mathnet.ru/eng/mzm9937 https://www.mathnet.ru/eng/mzm/v12/i6/p717
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Abstract page: | 142 | Full-text PDF : | 62 | First page: | 1 |
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