Glasnik Matematicki, Vol. 46, No.1 (2011), 71-77.

ON FINITE p-GROUPS CONTAINING A MAXIMAL ELEMENTARY ABELIAN SUBGROUP OF ORDER p2

Yakov Berkovich

Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel


Abstract.   We continue investigation of a p-group G containing a maximal elementary abelian subgroup R of order p2, p>2, initiated by Glauberman and Mazza [6]; case p=2 also considered. We study the structure of the centralizer of R in G. This reduces the investigation of the structure of G to results of Blackburn and Janko (see references). Minimal nonabelian subgroups play important role in proofs of Theorems 2 and 5.

2000 Mathematics Subject Classification.   20D15.

Key words and phrases.   Minimal nonabelian p-group, maximal elementary abelian subgroup, soft subgroup.


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DOI: 10.3336/gm.46.1.09


References:

  1. Y. Berkovich, Groups of prime power order. Vol. 1, Walter de Gruyter, Berlin, 2008.
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  2. Y. Berkovich and Z. Janko, Groups of prime power order. Vol. 2, Walter de Gruyter, Berlin, 2008.
    MathSciNet    

  3. Y. Berkovich and Z. Janko, Groups of prime power order. Vol. 3, Walter de Gruyter, Berlin, 2011.

  4. N. Blackburn, Generalizations of certain elementary theorems on p-groups, Proc. London Math. Soc. (3) 11 (1961), 1-22.
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  9. Z. Janko, Finite 2-groups with small centralizer of an involution, 2, J. Algebra 245 (2001), 413-429.
    MathSciNet     CrossRef

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