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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Turau, V. The 2-length of the hughes subgroup. Israel J. Math. 62, 206–212 (1988). https://doi.org/10.1007/BF02787122
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DOI: https://doi.org/10.1007/BF02787122