A campanological problem in group theory. II
Published online by Cambridge University Press: 24 October 2008
Extract
1. Let E be a finite non-null set and write (E) for the family of all permutations of E. Let
be a non-null subset of
(E) and write
(
) for the subgroup of
(E) generated by the members of
. For any α ∈
we put
so that (
) is a subgroup of
(
) and is independent of the choice of α in
. We suppose that E splits into k disjoint transitivity sets (orbits) Ei(1 ≤ i ≤ k) with respect to
(
); thus σEi = Ei for all σ ∈
(
).
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 1 , January 1966 , pp. 11 - 18
- Copyright
- Copyright © Cambridge Philosophical Society 1966
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