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
N. Blackburn,Groups of prime power order having an abelian centralizer of type (r, 1), Monatshefte für Mathematik99 (1985), 1–18.
Z. Janko,Finite 2-groups with small centralizer of an involution, Journal of Algebra241 (2001), 818–826.
Z. Janko,Finite 2-groups with small centralizer of an involution, 2, Journal of Algebra245 (2001), 413–429.
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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