Abstract
For a (finite) groupG and some prime powerp n, theH np -subgroupH pn (G) is defined byH np (G)=〈xεG|x pn≠1〉. A groupH≠1 is called aH np -group, if there is a finite groupG such thatH is isomorphic toH np (G) andH np (G)≠G. It is known that the Fitting length of a solvableH np -group cannot be arbitrarily large: Hartley and Rae proved in 1973 that it is bounded by some quadratic function ofn. In the following paper, we show that it is even bounded by some linear function ofn. In view of known examples of solvableH np -groups having Fitting lengthn, this result is “almost” best possible.
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Meixner, T. The fitting length of solvableH pn-groups. Israel J. Math. 51, 68–78 (1985). https://doi.org/10.1007/BF02772958
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DOI: https://doi.org/10.1007/BF02772958