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Irreducible products of characters in \(A_ n\). (English) Zbl 0796.20011

The author continues his work on the decomposition of products of ordinary irreducible characters. In the present paper he focuses attention on characters of alternating groups, looking for products that are irreducible. He shows that such a product \(\chi\psi\), being irreducible, occurs if and only if the degree \(n \geq 5\) of the alternating group \(A_ n\) is a perfect square.

MSC:

20C30 Representations of finite symmetric groups
20C15 Ordinary representations and characters
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References:

[1] Isaacs, I. M., Character Theory of Finite Groups (1976), New York: Academic Press, New York · Zbl 0337.20005
[2] James, G.; Kerber, A., The Representation Theory of the Symmetric Group, Encyclopedia of Mathematics and its Applications (1981), Mass.: Addison-Wesley, Mass. · Zbl 0491.20010
[3] [Z1] I. Zisser,The character covering numbers of the alternating group, to appear in J. Algebra.
[4] [Z2] I. Zisser,Squares of characters with a small number of irreducible constituents, to appear in J. Algebra. · Zbl 0776.20004
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