Electronic Resource
Springer
Journal of algebraic combinatorics
5 (1996), S. 315-322
ISSN:
1572-9192
Keywords:
Permutation group
;
cycle
;
Hopf algebra
;
Fourier series
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1022444515331
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