The Average Sylow Multiplicity Character and the Solvable Residual |
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Authors: | Dan Levy |
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Affiliation: | 1. The School of Computer Sciences , The Academic College of Tel-Aviv-Yaffo , Tel-Aviv , Israel danlevy@trendline.co.il |
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Abstract: | Let G be a finite group, and let p1,…, pm be the distinct prime divisors of |G|. Given a sequence 𝒫 =P1,…, Pm, of Sylow pi-subgroups of G, and g ∈ G, denote by m𝒫(g) the number of factorizations g = g1…gm such that gi ∈ Pi. The properly normalized average of m𝒫 over all 𝒫 is a complex character over G whose kernel contains the solvable radical of G [7 Levy , D. ( 2010 ). The average Sylow multiplicity character and solvability of finite groups . Communications in Algebra. 38 : 632 – 644 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]. The present paper characterizes the solvable residual of G in terms of this character. |
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Keywords: | Characters Finite groups Solvable residual Sylow subgroups |
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