Even permutations as a product of two elements of order five |
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Institution: | 10 Phillips Road, Palo Alto, California 94303 USA;Department of Mathematics, C-012, University of California at San Diego, La Jolla, California 92093 USA |
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Abstract: | Let An denote the alternating group on n symbols. If n = 5, 6, 7, 10, 11, 12, 13 or n ⩾ 15, every permutation in An is the product of two elements of order 5 in An. The same is true for n ⩽ 14, except for thirteen types of permutations, namely 31, 22, 24, 33, 213141, 2251, 2541, 11, 12, 13, 14, 3111, 2411. (For example, the permutation (12)(34)(56)(78)(9) is not the product of two elements of order 5 in A9.) |
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