Open Access
2010 Minimal Permutation Representations of Nilpotent Groups
Ben Elias, Lior Silberman, Ramin Takloo-Bighash
Experiment. Math. 19(1): 121-128 (2010).


A minimal permutation representation of a finite group $G$ is a faithful $G$-set with the smallest possible size. We study the structure of such representations and show that for certain groups they may be obtained by a greedy construction. In these situations (except when central involutions intervene) all minimal permutation representations have the same set of orbit sizes. Using the same ideas, we also show that if the size $d(G)$ of a minimal faithful $G$-set is at least $c|G|$ for some $c>0$, then $d(G) = |G|/m + O(1)$ for an integer $m$, with the implied constant depending on $c$.


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Ben Elias. Lior Silberman. Ramin Takloo-Bighash. "Minimal Permutation Representations of Nilpotent Groups." Experiment. Math. 19 (1) 121 - 128, 2010.


Published: 2010
First available in Project Euclid: 12 March 2010

zbMATH: 1188.20001
MathSciNet: MR2649988

Primary: 20B35 , 20D15
Secondary: 20D30 , 20D60

Keywords: lattices , nilpotent groups , Permutation representations

Rights: Copyright © 2010 A K Peters, Ltd.

Vol.19 • No. 1 • 2010
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