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Some criteria for the decomposability of finite groups

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Abstract

In this paper we prove the following fundamental results.Theorem 1: A finite unsolvable group, every involution of which is contained in a proper isolated subgroup, is decomposable.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), qodd.

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Authors and Affiliations

  1. Krasnoyarsk State University, USSR

    V. M. Busarkin & N. D. Podufalov

Authors
  1. V. M. Busarkin
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  2. N. D. Podufalov
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Translated from Matematicheski Zametki, Vol. 12, No. 6, pp. 717–725, December, 1972.

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Busarkin, V.M., Podufalov, N.D. Some criteria for the decomposability of finite groups. Mathematical Notes of the Academy of Sciences of the USSR 12, 871–875 (1972). https://doi.org/10.1007/BF01156047

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  • DOI: https://doi.org/10.1007/BF01156047

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