FINITE GROUPS WITH MULTIPLICITY-FREE PERMUTATION CHARACTERS
2005 ◽
Vol 04
(02)
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pp. 187-194
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Let G be a finite group and H a subgroup of G. The Hecke algebra ℋ(G,H) associated with G and H is defined by the endomorphism algebra End ℂ[G]((ℂH)G), where ℂH is the trivial ℂ[H]-module and (ℂH)G = ℂH⊗ℂ[H] ℂ[G]. As is well known, ℋ(G,H) is a semisimple ℂ-algebra and it is commutative if and only if (ℂH)G is multiplicity-free. In [6], by a ring theoretic method, it is shown that if the canonical involution of ℋ(G,H) is the identity then ℋ(G,H) is commutative and, if there exists an abelian subgroup A of G such that G = AH then ℋ(G,H) is commutative. In this paper, by a character theoretic method, we consider the commutativity of ℋ(G,H).
2016 ◽
Vol 15
(03)
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pp. 1650053
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1982 ◽
Vol 92
(1)
◽
pp. 55-64
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2011 ◽
Vol 14
◽
pp. 232-237
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2019 ◽
Vol 18
(08)
◽
pp. 1950159
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1985 ◽
Vol 37
(3)
◽
pp. 442-451
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1969 ◽
Vol 10
(3-4)
◽
pp. 359-362
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