Author： Langley Thomas Levitt David Rower Joseph
Publisher： Mathematical Association of America
ISSN： 1930-0980
Source： Mathematics Magazine, Vol.84, Iss.2, 2011-04, pp. : 128-136
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Abstract
The probability that two elements in a nonabelian finite group commute is at most 5/8, and this bound is realized exactly when the center of the group is one fourth of the group. We generalize this result by finding similar bounds on the probability that a product of several group elements is equal to its reverse, and the probability that a product is equal to at least one cyclic rearrangement of itself. Both of these naturally extend the 5/8 bound.
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