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On a question of N. Blackburn about finite 2-groups

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Abstract

We classify finite 2-groupsG possessing an involution which is contained in a unique subgroup of order 4 inG. This answers a question of N. Blackburn about finite 2-groups. We show that the extended Blackburn’s problem is reduced to the outstanding problem ofp-group theory to classify 2-groups with exactly three involutions.

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References

  1. N. Blackburn,Groups of prime power order having an abelian centralizer of type (r, 1), Monatshefte für Mathematik99 (1985), 1–18.

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  2. Z. Janko,Finite 2-groups with small centralizer of an involution, Journal of Algebra241 (2001), 818–826.

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  3. Z. Janko,Finite 2-groups with small centralizer of an involution, 2, Journal of Algebra245 (2001), 413–429.

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Authors and Affiliations

  1. Faculty of Civil Engineering and Architecture, University of Split, 21000, Split, Croatia

    Zdravka Božikov

  2. Mathematical Institute, University of Heidelberg, 69120, Heidelberg, Germany

    Zvonimir Janko

Authors
  1. Zdravka Božikov
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  2. Zvonimir Janko
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Božikov, Z., Janko, Z. On a question of N. Blackburn about finite 2-groups. Isr. J. Math. 147, 329–331 (2005). https://doi.org/10.1007/BF02785370

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  • DOI: https://doi.org/10.1007/BF02785370

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