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Groups with relatively small normalizers of biprimary subgroups

Abstract

We study groups in which, either for any biprimary or for any nonprimary subgroup, the following condition is fulfilled: The index of the product of a subgroup and its centralizer in the normalizer of the subgroup is divisible by some prime number fixed for a group. We obtain the complete description of such groups.

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Correspondence to V. A. Antonov.

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Original Russian Text © V.A. Antonov and T.G. Nozhkina, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 8, pp. 3–13.

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Antonov, V.A., Nozhkina, T.G. Groups with relatively small normalizers of biprimary subgroups. Russ Math. 57, 1–9 (2013). https://doi.org/10.3103/S1066369X1308001X

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  • DOI: https://doi.org/10.3103/S1066369X1308001X

Keywords and phrases

  • group
  • subgroup
  • biprimary subgroup
  • nonprimary subgroup
  • centralizer
  • normalizer
  • index