Cycle-Closed Permutation Groups |
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Authors: | Peter J Cameron |
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Institution: | (1) School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, E1 4NS London, UK |
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Abstract: | A finite permutation group is cycle-closed if it contains all the cycles of all of its elements. It is shown by elementary
means that the cycle-closed groups are precisely the direct products of symmetric groups and cyclic groups of prime order.
Moreover, from any group, a cycle-closed group is reached in at most three steps, a step consisting of adding all cycles of
all group elements. For infinite groups, there are several possible generalisations. Some analogues of the finite result are
proved. |
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Keywords: | Permutation group cycle Hopf algebra Fourier series |
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