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Archiv der Mathematik

, Volume 68, Issue 1, pp 7–16 | Cite as

A class of special p-groups

  • Libero Verardi
Article
  • 98 Downloads

Abstract

Starting by the multiplication table of a finite group G, for each odd prime p a special p-group P of exponent p is constructed. Some connections between the structures of G and P, concerning subgroups and automorphisms, are given. When p does not divide the order of G, for every normal subgroup of G a direct decomposition of P is done. Besides, the order of the derived subgroup of G is proved to be connected with the existence of some abelian subgroups of maximal order in P. Finally, the elements of P with large centralizers are characterized in terms of algebraic properties of the multiplication table of G.

Keywords

Normal Subgroup Finite Group Abelian Subgroup Maximal Order Permutation Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    R. Cortini, On special p-groups (submitted).Google Scholar
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    H. Heineken and H. Liebeck, The occurrence of finite groups in the automorphism group of nilpotent groups of class 2. Arch. Math. 24, 8–16 (1973).CrossRefMathSciNetGoogle Scholar
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    B. Huppert, Endliche Gruppen I. Berlin-Heidelberg-New York 1967.Google Scholar
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    U. H. M. Webb, The occurrence of groups as automorphisms of nilpotent p-groups. Arch. Math. 37, 481–489(1981).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Verlag 1997

Authors and Affiliations

  • Libero Verardi
    • 1
  1. 1.Dipartimento di MatematicaUniversità degli Studi di BolognaBolognaItaly

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