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The 2-length of the hughes subgroup

Authors:	Volker Turau

Institution:	1. Institut für Informatik III, Universit?t Karlsruhe, 7200, Karlsruhe, FRG

Abstract:	For a finite groupG and some prime powerp ⁿ, the $H_{p^n }$ -subgroup $H_{p^n } \left( G \right)$ is defined by $H_{p^n } \left( G \right) = \left\langle {\chi \varepsilon G\|\chi ^{p^n } \ne 1} \right\rangle$ . Meixner proved that ifG is a finite solvable group and $G \ne H_{2^n } \left( G \right)$ for somen≧1, then the Fitting length of $H_{2^n } \left( G \right)$ is bounded by 4n. In the following note it is shown that the 2-length of $H_{2^n } \left( G \right)$ is at mostn. This result cannot be derived from Meixner’s paper, since his result implies only that the 2-length is bounded by 2n.

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