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A campanological problem in group theory. II

Published online by Cambridge University Press:  24 October 2008

R. A. Rankin
R. A. Rankin
Affiliation:
University of Glasgow
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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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References

REFERENCES

(1)Burns, J.The abstract groups of degree 8. American J. Math. 37 (1915), 195–214.CrossRefGoogle Scholar
(2)Rankin, R. A.A campanological problem in group theory. Proc. Cambridge Philos. Soc. 44 (1948), 17–25.CrossRefGoogle Scholar