On Burnside’s lemma
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- by Marcel Herzog PDF
- Proc. Amer. Math. Soc. 28 (1971), 379-380 Request permission
Abstract:
Burnside’s lemma on characters of finite groups is generalized, leading to the following theorem: if $G$ is a simple group of order divisible by exactly 3 primes, and if one of the Sylow subgroups of $G$ is cyclic, then for each Sylow subgroup $P$ of $G$ we have ${C_G}(P) = Z(P)$.References
- Richard Brauer, On simple groups of order $5\cdot 3^{a}\cdot 2^{b}$, Bull. Amer. Math. Soc. 74 (1968), 900–903. MR 236255, DOI 10.1090/S0002-9904-1968-12073-7
- Walter Feit, Characters of finite groups, W. A. Benjamin, Inc., New York-Amsterdam, 1967. MR 0219636
- Marcel Herzog, On finite groups with cyclic Sylow subgroups for all odd primes, Israel J. Math. 6 (1968), 206–216. MR 235037, DOI 10.1007/BF02760253
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 379-380
- MSC: Primary 20.43
- DOI: https://doi.org/10.1090/S0002-9939-1971-0274589-1
- MathSciNet review: 0274589