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On the group of
permutations with countable support
Justin Thomas Lloyd and William Smiley |
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Vol. 58 (1975), No. 2, 529–530
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Abstract |
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Let SX denote the group of permutations of the set X. If ℵα is an infinite cardinal, the set of permutations having support with cardinality less than or equal to ℵα is a normal subgroup of SX. The principal result of this paper is a constructive proof that SX is generated by its cycles, if X is countably infinite. Of particular interest is the corollary that for any set X, the cycles of SX generate the subgroup of permutations with countable support. |
Mathematical Subject Classification
Primary: 20F15
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Milestones
Received: 2 January 1974
Published: 1 June 1975
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Authors |
| Justin Thomas Lloyd | |
| William Smiley | |
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