Minimum simplicial complexes with given abelian automorphism group

Author:
Zevi Miller

Journal:
Trans. Amer. Math. Soc. **271** (1982), 689-718

MSC:
Primary 05C65; Secondary 20B25

DOI:
https://doi.org/10.1090/S0002-9947-1982-0654857-3

MathSciNet review:
654857

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Abstract: Let be a pure -dimensional simplicial complex. Let be the automorphism group of , and let be the group of permutations on -cells of induced by the elements of . Given an abelian group we consider the problem of finding the minimum number of points in such that , and the minimum number of -cells in such that . Write , where each factor appears times in the canonical factorization of . For containing no factors satisfying we find that when , and we derive upper bounds for and in the remaining possibilities for and .

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DOI:
https://doi.org/10.1090/S0002-9947-1982-0654857-3

Article copyright:
© Copyright 1982
American Mathematical Society