A Note on Orbits of Subgroups of the Permutation Groups
Canadian journal of mathematics, Tome 38 (1986) no. 2, pp. 277-285
Voir la notice de l'article provenant de la source Cambridge University Press
In [2] we studied Milgram's Complex, C(n – 1), which was first defined in [3], in the following manner. Let Sn , the permutation group of n symbols, act on R n in the obvious manner; put α(x) = (y), where yi = xα –1(i) . Let s = (1, 2, ..., n), then C(n – 1) is the convex hull of the points α(s), α ∊ Sn . Here we shall generalise this construction as follows. Let G be a subgroup of Sn , and let v ∊ R n . Then C(G, v) is the convex hull of α(v), α ∊ G. We prove invariance over v subject to certain restrictions, give counter-examples to shew lack of invariance if we alter G, discuss how we may describe C(G, v), shew that the only “nice” case is essentially when G is Sn , and lastly give some examples.
Leitch, R. D. A Note on Orbits of Subgroups of the Permutation Groups. Canadian journal of mathematics, Tome 38 (1986) no. 2, pp. 277-285. doi: 10.4153/CJM-1986-013-5
@article{10_4153_CJM_1986_013_5,
author = {Leitch, R. D.},
title = {A {Note} on {Orbits} of {Subgroups} of the {Permutation} {Groups}},
journal = {Canadian journal of mathematics},
pages = {277--285},
year = {1986},
volume = {38},
number = {2},
doi = {10.4153/CJM-1986-013-5},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1986-013-5/}
}
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