论文信息 - Proportions of elements with given 2-part order in the symmetric group

Proportions of elements with given 2-part order in the symmetric group

Abstract. For an element g in a group X, we say that g has 2-part order if is the largest power of 2 dividing the order of g. Using results of Erdős and Turán, and Beals et al., we give explicit lower bounds on the proportion of elements of the symmetric group with certain 2-part orders. Some of these lower bounds are constant; for example we show that at least 23.5% of the elements in () have a certain 2-part order and furthermore, more than half of the elements in have one of three 2-part orders. Also, for all , at least of the elements in have the same 2-part order and we show that is best possible.

Cheryl E. Praeger | C. Praeger | S. Guest | Simon Guest

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