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- W2047584013 abstract "Let A be a finite group and let n be the number of primes, including multiplicities, which divide the order of A. Suppose further that G is a finite solvable group which admits A as a fixed-point-free operator group and such that (i A I, G|I ) = 1. Under these assumptions it has been conjectured that l(G), the nilpotent length of G, is at most n, while lp(G), the p-length of G, is at most [(n+1)/2]. These inequalities have been verified and shown to be best-possible in certain special cases ( [3 ][5], [1]). It is the purpose of this note to show that these conjectured upper bounds are actually obtained provided A is solvable. Specifically we will prove" @default.
- W2047584013 created "2016-06-24" @default.
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- W2047584013 date "1968-06-01" @default.
- W2047584013 modified "2023-09-23" @default.
- W2047584013 title "A note on fixed-point-free solvable operator groups" @default.
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- W2047584013 doi "https://doi.org/10.1090/s0002-9939-1968-0231909-1" @default.
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