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Let p be an odd prime number and G a finite p-group. We prove that if the rank of G is greater than p, then G has no maximal elementary abelian subgroup of rank 2. It follows that if G has rank greater than p, then the poset of elementary abelian subgroups of G of rank at least 2 is connected and the torsion-free rank of the group of endotrivial kG-modules is one, for any field k of characteristic p. We also verify the class-breadth conjecture for the p-groups G whose poset has more than one component

Year: 2010

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oai:eprints.lancs.ac.uk:33515

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- (1934). A Contribution to the Theory of Groups of Prime-Power Order,
- (1976). Character theory of groups,
- (1976). Character theory of finite groups,
- (2008). Connected components of the category of elementary abelian subgroups,
- (1975). Counting Abelian Subgroups of p-groups.
- (1967). Endliche Gruppen, I,
- (2006). Endotrivial modules for groups of Lie type,
- (2006). Endotrivial modules for finite groups of Lie type,
- (1968). Finite Groups, Harper and Row,
- (1985). Groups of prime-power order having an abelian centralizer of type (r, 1),
- (1985). Groups of prime-power order having an abelian centralizer of type (r;1),
- (2008). Groups of prime-power order, Volume I, Walter de Gruyter,
- (1998). Khukhro, p-automorphisms of p-groups, London Mathematical Society Lecture Note Series 246,
- (1998). Khukhro, p-automorphisms of finite p-groups, London Mathematical Society Lecture Note Series 246,
- (1998). Limits of abelian subgroups of p-groups,
- (1998). Limits of abelian subgroups of finite p-groups,
- (2007). Maximal elementary abelian subgroups of rank 2,
- (1970). On 2-groups with no normal abelian subgroups of rank 3, and their occurrence as Sylow 2-subgroups of simple groups,
- (1970). On 2-groups with no normal abelian subgroups of rank 3, and their occurrence as Sylow 2-subgroups of finite simple groups,
- (1990). On subgroups of p-groups having soft subgroups,
- (1984). Soft subgroups of p-groups,
- (1963). Solvability of groups of odd order,
- (1969). The breadth and the class of a p-group,
- (1969). The breadth and the class of a finite p-group,
- (2006). The class-breadth conjecture revisited,
- (2004). The classi of endo-trivial modules,
- (2004). The classification of endo-trivial modules,
- (1959). The theory of groups,
- (1958). The theory of groups, Second edition,

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