Conjugacy of Odd order Hall Subgroups

Let the group G = AB be a product of two π-decomposable sub-where π is a set of primes. The authors conjecture thatif π is a set of odd primes. In this paper it is proved that the conjecture is true if A and B are soluble. A similar result with certain additional restrictions holds in the case 2 ∈ π. Moreover, it is shown that the conjecture holds if O π (A) and O π (B) have coprime orders.

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“…Since π is a set of odd primes, then M satisfies the C π -property by [8,Theorem A] and so, by the Frattini argument, we conclude that…”

Section: This Is Clear Sincementioning

confidence: 98%

“…• N ∼ = L 3 (8). In this case |N | = 2 9 · 3 2 · 7 2 · 73 and by [2, Lemma 2.5] we may assume that |N ∩ A| divides 73 · 3 and |N ∩ B| divides 2 9 · 7 2 .…”

Section: Assume That This Is Not True and Takementioning

confidence: 99%

On the product of two π-decomposable soluble groups

Kazarin¹,

Martínez-Pastor²,

Pérez‐Ramos³

2009

Publicacions Matemàtiques

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“…In this case n\(G) -n(2f (q + y/2q + 1)) or TT,(G) = TT(2/(<7 -JTq + 1)) depending if / = 1, 7 (8) o r / = 3, 5 (8). In both cases there should exists a n(2(q ± y/2q + 1)-Hall subgroup of 5 and this is not possible in any of the two cases (see [12] or [25]).…”

Section: Almost Simple Groupsmentioning

confidence: 99%

“…It is well known that G is a soluble group if and only if G has a 7r-Hall subgroup for any set of primes n. If G is not soluble, the existence of some Hall subgroups have been proved in several papers (see, for example, [9,23,8]). We prove the following theorem on the existence of a jri-Hall subgroup.…”

Section: Introductionmentioning

confidence: 99%

Finite group with Hall coverings

Jabara

Lucido

2005

J. Aust. Math. Soc.

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“…https://doi.org/10.1017/S1446788700008624 [9] Finite p-nilpotent groups with some subgroups c-supplemented 437…”

Section: Applicationsmentioning

confidence: 99%

Finite p–nilpotent groups with some subgroups c–supplemented

Guo

Shum

2005

J. Aust. Math. Soc.

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A subgroup H of a finite group G is said to be c–supplemented in G if there exists a subgroup K of G such that G = HK and H∩K is contained in coreG (H). In this paper some results for finite p–nilpotent groups are given based on some subgroups of Pc–supplemented in G, where p is a prime factor of the order of G and P is a Sylow p–subgroup of G. We also give some applications of these results.

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Conjugacy of Odd order Hall Subgroups

Cited by 104 publications

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On the product of two π-decomposable soluble groups

On the product of two π-decomposable soluble groups

Finite group with Hall coverings

Finite p–nilpotent groups with some subgroups c–supplemented

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Conjugacy of Odd order Hall Subgroups

Cited by 104 publications

References 0 publications

On the product of two &pi;-decomposable soluble groups

On the product of two &pi;-decomposable soluble groups

Finite group with Hall coverings

Finite p–nilpotent groups with some subgroups c–supplemented

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On the product of two π-decomposable soluble groups

On the product of two π-decomposable soluble groups