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Siberian Mathematical Journal

, Volume 49, Issue 2, pp 218–221 | Cite as

Involutory decomposition of a group and twisted subsets with few involutions

  • D. V. VeprintsevEmail author
  • A. L. Myl’nikov
Article
  • 27 Downloads

Abstract

A subset K of some group C is called twisted if 1 ∈ K and x, yK implies that xy −1 x belongs to K. We use the concept of twisted subset to investigate and generalize the concept of involutory decomposition of a group. A group is said to admit involutory decomposition if it contains some involution such that the group is the product of the centralizer of the involution and the set of elements inverted by the involution. We study the twisted subsets with at most one involution. We prove that if a twisted subset has no involutions at all then it generates a subgroup of odd order.

Keywords

involutory decomposition of a group twisted subset twisted subgroup 

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References

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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Krasnoyarsk Agricultural State UniversityKrasnoyarskRussia
  2. 2.Siberian Federal UniversityKrasnoyarskRussia

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