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A note on generalized characters
Published online by Cambridge University Press: 17 April 2009
Abstract
Let α be a generalized character of a (not necessarily finite) group G over an arbitrary field, and n a positive integer. It is shown that the function α(n) defined by α(n) (g) = α(gn) is also a generalized character of G. An application confirms a conjecture of Robert Higgins and David Ballew: if G is finite and k is also a positive integer, the k-th power of the number of n-th roots of g, summed over all g in G, is divisible by the order of G.
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- Copyright © Australian Mathematical Society 1971
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