Vol. 45, No. 2, 1973

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On the number of type-k translation-invariant groups

Joel Saul Hillel

Vol. 45 (1973), No. 2, 539–541
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-k 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 Xk 1 over the two-element field.

Mathematical Subject Classification 2000
Primary: 20B05
Milestones
Received: 14 November 1971
Published: 1 April 1973
Authors
Joel Saul Hillel