Finite 2-groups with a nonabelian Frattini subgroup of order 16 |
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Authors: | Zdravka Bo?ikov |
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Institution: | (1) Faculty of Civil Engineering and Architecture, University of Split, 21000 Split, Croatia |
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Abstract: | According to a classical result of Burnside, if G is a finite 2-group, then the Frattini subgroup Φ(G) of G cannot be a nonabelian group of order 8. Here we study the next possible case, where G is a finite 2-group and Φ(G) is nonabelian of order 16. We show that in that case Φ(G) ≅ M × C2, where M ≅ D8 or M ≅ Q8 and we shall classify all such groups G (Theorem A).
Received: 16 February 2005; revised: 7 March 2005 |
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Keywords: | 20D15 |
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