MULTIPLICITIES IN SYLOW SEQUENCES AND THE SOLVABLE RADICAL
2008 ◽
Vol 78
(3)
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pp. 477-486
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AbstractA complete Sylow sequence, 𝒫=P1,…,Pm, of a finite group G is a sequence of m Sylow pi-subgroups of G, one for each pi, where p1,…,pm are all of the distinct prime divisors of |G|. A product of the form P1⋯Pm is called a complete Sylow product of G. We prove that the solvable radical of G equals the intersection of all complete Sylow products of G if, for every composition factor S of G, and for every ordering of the prime divisors of |S|, there exist a complete Sylow sequence 𝒫 of S, and g∈S such that g is uniquely factorizable in 𝒫 . This generalizes our results in Kaplan and Levy [‘The solvable radical of Sylow factorizable groups’, Arch. Math.85(6) (2005), 490–496].
2010 ◽
Vol 20
(07)
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pp. 847-873
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2016 ◽
Vol 10
(02)
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pp. 1750024
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2018 ◽
Vol 17
(07)
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pp. 1850122
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2017 ◽
Vol 16
(03)
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pp. 1750051
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Keyword(s):
2006 ◽
Vol 343
(6)
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pp. 387-392
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