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Finite groups with biprimary subgroups of a definite form

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Abstract

The paper studies the structure of finite groups in which, for any biprimary subgroup B, eitherl 2(B) ≤ 1 or O2(B) is a metacyclic group. As a corollary of the result obtained here and of known results of other authors, a description is adduced of finite simple groups in which the intersection of any two distinct Sylow 2-subgroups is metacyclic.

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Literature cited

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Translated from Matematicheskie Zametki, Vol. 14, No. 6, pp. 853–858, December, 1973.

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Belonogov, V.A. Finite groups with biprimary subgroups of a definite form. Mathematical Notes of the Academy of Sciences of the USSR 14, 1049–1051 (1973). https://doi.org/10.1007/BF01099590

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Keywords

  • Finite Group
  • Simple Group
  • Definite Form
  • Finite Simple Group
  • Metacyclic Group