Nilpotent Partition-Inducing Automorphism Groups
Canadian journal of mathematics, Tome 33 (1981) no. 2, pp. 412-420
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If A is a group acting on a set X and x ∈ X, we denote the stabilizer of x in A by CA(x) and let Γ(x) be the set of elements of X fixed by CA(x). We shall say the action of A is partitive if the distinct subsets Γ(x), x ∈ X, partition X. A special example of this phenomenon is the case of a semiregular action (when CA (x) = 1 for every x ∈ X so the induced partition is a trivial one). Our concern here is with the case that A is a group of automorphisms of a finite group G and X = G#, the set of non-identity elements of G. We shall prove that if A is nilpotent, then except in a very restricted situation, partitivity implies semiregularity.
Pettet, Martin R. Nilpotent Partition-Inducing Automorphism Groups. Canadian journal of mathematics, Tome 33 (1981) no. 2, pp. 412-420. doi: 10.4153/CJM-1981-036-2
@article{10_4153_CJM_1981_036_2,
author = {Pettet, Martin R.},
title = {Nilpotent {Partition-Inducing} {Automorphism} {Groups}},
journal = {Canadian journal of mathematics},
pages = {412--420},
year = {1981},
volume = {33},
number = {2},
doi = {10.4153/CJM-1981-036-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-036-2/}
}
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