On weakly h-subgroups of finite groups ii

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August undefined, 2024

Web27 de set. de 2012 · A subgroup H of G is called weakly ℋ-subgroup in G if there exists a normal subgroup K of G such that G = HK and H ∩ K is an ℋ-subgroup in G. In this … WebA subgroup H of G is called an H -subgroup in G if N G ( H) ∩ H x ≤ H for all x ∈ G. Furthermore, a subgroup H of G is called a weakly H -subgroup in G if there exists a …

On weakly ℋC-embedded subgroups of finite groups Journal of …

WebWe say that a subgroup H of G is weakly σ -semipermutable in G if there exists a σ -permutable subgroup T of G such that HT is σ -permutable in G and H ∩ T ≤ H σ s G, where H σ s G is the subgroup of H generated by all those subgroups of H which are σ -semipermutable in G. Web21 de jun. de 2024 · A subgroup H of a finite group G is said to be weakly \ (\mathcal {M}\)-supplemented in G if there exists a subgroup B of G such that (1) \ (G=HB\) and (2) \ (H_1B = BH_1 ionescu ethnicity

SS-QUASINORMAL SUBGROUPS OF FINITE GROUPS

WebLemma 2.6. If the Sylow 2-subgroups of H ∩K are non-abelian, let y be a cyclic sub-group of H∩K with order 4. It is clear that at this time the Sylow 2-subgroups of H are also non-abelian and y is a cyclic subgroup of H with order 4. Then, by the hypothesis, y either is weakly s-supplementally embedded or has a supersolvable supplement in G. WebOn weakly -subgroups of finite groups II* @article{Chen2024OnW, title={On weakly -subgroups of finite groups II*}, author={Ruifang Chen and Xiaoli Li and Xianhe Zhao}, … Web1 de dez. de 2014 · In particular, when \ (H\) is a subgroup of prime-power order and \ (K\) is a Sylow subgroup containing it, \ (H\) is simply said to be a weakly closed subgroup of \ (G\) or weakly closed... ionesco the lesson

$On ${\mathcal{F}}$ -supplemented subgroups of finite groups$

On weakly -supplemented subgroups of finite groups

Webon weaklySS-quasinormal subgroups of finite groups 65 Proof. Suppose that the result is false and letGbe a counterexample of minimal order. We treat with the following two cases: Case 1. Every cyclic subgroupHofPwith prime order or order 4 (ifPis a non-abelian 2-group andH*Z1(G)) without ap-nilpotent supplement inGis weaklySS-quasinormal inG. Web8 de dez. de 2024 · Abstract. A subgroup H of a finite group G is weakly-supplemented in G if there exists a proper subgroup K of G such that G = HK. In the paper, we extend one … ontario license sticker renewal refundWebLemma 2.6. If the Sylow 2-subgroups of H ∩K are non-abelian, let y be a cyclic sub-group of H∩K with order 4. It is clear that at this time the Sylow 2-subgroups of H are also non … ontario license plates types

"Webclass of all supersolvable groups, and G a group with E as a normal subgroup of G such that G=E 2F. Suppose that P has a subgroup D such that 1 " - On weakly h-subgroups of finite groups ii

On weakly h-subgroups of finite groups ii

Web3 de jun. de 2016 · We say that H is weakly ℋ -embedded in G if G has a normal subgroup K such that HG = HK and H ∩ K is an ℋ-subgroup in G. In this paper, we investigate the … Web25 de mai. de 2012 · We investigate the influence of weakly s-normal subgroups on the structure of finite groups. Some recent results are generalized and unified. Assume that …

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Web16 de nov. de 2024 · A subgroup H of G is called weakly normal in G if H^ {x}\le N_ {G} (H) implies that H=H^ {x}, where x\in G. Here we prove that for p -subgroups of finite groups, the concept of pronormal subgroups, weakly normal subgroups and weakly closed subgroups are equivalent. Theorem 4.3 Web1 de nov. de 2012 · A subgroup H of G is called a weakly -subgroup in G if there exists a normal subgroup K of G such that G = HK and H ∩ K is an -subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly -subgroup in G.

Webcharacterize the solvable T-group by H-subgroups. Theorem 1.1 ([6]). Let G be a group. The following statements are equivalent: (i) G is a solvable T-group; (ii) Every subgroup of G is an H-subgroup of G; (iii) For all p A pðGÞ, the p-subgroups of G are H-subgroups of G. Another important concept (Deﬁnition 1.2 below) was introduced by ... WebA subgroup H of a group G is said to be weakly M -supplemented in G if there exists a subgroup B of G provided that (1) G = HB, and (2) if H 1 / H G is a maximal subgroup of H / H G, then H 1 B = B H 1 < G, where HG is the largest normal subgroup of G contained in H.

WebON WEAKLY M-SUPPLEMENTED SUBGROUPS OF SYLOW p-SUBGROUPS OF FINITE GROUPS∗ LONG MIAO School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, P. R. China e-mail: [email protected] (Received 25 August 2009; revised 21 September 2010; accepted 2 November 2010) Abstract. A subgroup H is … Web1 de set. de 2014 · Abstract. A subgroup H of a group G is said to be weakly normal in G if H g ≤N G (H) implies that g∈N G (H). In this paper, using the condition that the minimal …

Web5 de jul. de 2013 · II. With applications to inite groups and orders. John Wiley & Sons, Inc., New York, 1987. [21] M. R., Darafsheh. Maximal subgroups of the group GL6 (2). Bull. Malaysian Math.Soc. (2) 7 ( 1984 ), 49–55. Google Scholar [22] Leonard Eugene, Dickson. Linear groups, with an exposition of the Galois field theory.

WebWe show that stationary characters on irreducible lattices of higher-rank connected semisimple Lie groups are conjugation invariant, that is, they are genuine characters. This result has several applications in repres… ontario life insurance actWeb4 de jul. de 2009 · We say that: (1) H is τ-quasinormal in G if H permutes with all Sylow subgroups Q of G such that ( Q , H ) = 1 and ( H , Q G ) ≠ 1; (2) H is weakly τ … ontario license sticker renewal reminderWeb2 de out. de 2016 · Request PDF On Weakly ℋ-embedded Subgroups of Finite Groups Let G be a finite group and H a subgroup of G. We say that H is an ℋ-subgroup in G if … ionesco the leaderWeb31 de ago. de 2024 · We introduce the concept of F h -supplemented subgroups and investigate the structure of finite groups on assuming that some maximal subgroups of … ontario lic plate renewalWebON WEAKLY S-PERMUTABLY EMBEDDED SUBGROUPS OF FINITE GROUPS HAORAN YU (Received 15 March 2016; accepted 19 March 2016; ﬁrst published online 21 July 2016) Abstract In this paper, we obtain some criteria for p-nilpotency and p-supersolvability of a ﬁnite group and extend some known results concerning weakly S … ionescu libertyWeb3 de jun. de 2016 · We say that H is weakly ℋ -embedded in G if G has a normal subgroup K such that H G = HK and H ∩ K is an ℋ-subgroup in G. In this paper, we investigate the … ontario license tag renewal ontario lieu of notice