ON WEAKLY -SUPPLEMENTED SUBGROUPS OF SYLOW p-SUBGROUPS OF FINITE GROUPS
2011 ◽
Vol 53
(2)
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pp. 401-410
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AbstractA subgroup H is called weakly -supplemented in a finite group G if there exists a subgroup B of G provided that (1) G = HB, and (2) if H1/HG is a maximal subgroup of H/HG, then H1B = BH1 < G, where HG is the largest normal subgroup of G contained in H. In this paper we will prove the following: Let G be a finite group and P be a Sylow p-subgroup of G, where p is the smallest prime divisor of |G|. Suppose that P has a non-trivial proper subgroup D such that all subgroups E of P with order |D| and 2|D| (if P is a non-abelian 2-group, |P : D| > 2 and there exists D1 ⊴ E ≤ P with 2|D1| = |D| and E/D1 is cyclic of order 4) have p-nilpotent supplement or weak -supplement in G, then G is p-nilpotent.
2014 ◽
Vol 57
(3)
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pp. 648-657
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2012 ◽
Vol 49
(3)
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pp. 390-405
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1970 ◽
Vol 3
(2)
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pp. 273-276
1969 ◽
Vol 21
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pp. 418-429
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1969 ◽
Vol 10
(3-4)
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pp. 359-362
1997 ◽
Vol 40
(2)
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pp. 243-246
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2008 ◽
Vol 01
(03)
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pp. 369-382
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2019 ◽
Vol 19
(05)
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pp. 2050093
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