On the number of type-<i>k</i>translation-invariant groups

Joel Hillel

Type: Article

Publication Date: 1973-04-01

Citations: 29

DOI: https://doi.org/10.2140/pjm.1973.45.539

Abstract

The concept of a translation-invariant permutation group was introduced in connection with the problem of constructing "algebras of symmetry-classes of tensors".Such a group is of type-Zc if it has k orbits.In this paper the number of type-k groups is shown to be the same as the number of divisors of X k -1 over the two-element field.Let £L be the group of all permutations of finite degree on the set {1, 2, 3, •}.If σ is the permutation given by (α 1 6 1 )(α 2 6 2 ) (#A), its translate σ m is defined to be the permutation {a, + 1 &! + l)(α 2 + 1 6 2 + 1) (α t + 1 b t + 1) .

Locations

Pacific Journal of Mathematics - View - PDF

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