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Elements of order at most 4 in finite 2-groups, 2
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Zvonimir Janko
Published/Copyright:
November 18, 2005
Abstract
Let G be a finite p -group. We show that if Ω2(G ) is an
extraspecial group then Ω2(G ) = G . If we assume only that 
(the subgroup generated by
elements of order p 2 ) is an extraspecial group, then the
situation is more complicated. If p = 2, then either
= G or G is a semidihedral group of order 16. If p > 2, then we can only show that = Hp(G ).
:
Published Online: 2005-11-18
Published in Print: 2005-11-18
Walter de Gruyter GmbH & Co. KG
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- Polynomial properties in unitriangular matrices. II
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- The number of non-solutions of an equation in a group
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Articles in the same Issue
- Elements of order at most 4 in finite 2-groups, 2
- On the number of infinite branches in the graph of all p-groups of coclass r
- Polynomial properties in unitriangular matrices. II
- Connectivity of the coset poset and the subgroup poset of a group
- The number of non-solutions of an equation in a group
- Groups, periodic planes and hyperbolic buildings
- Endomorphisms preserving an orbit in a relatively free metabelian group
- Generic units in abelian group rings
- Subgroup growth of Baumslag–Solitar groups
