[PDF] Top 20 On \(S\)-quasinormally embedded subgroups of finite groups
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On \(S\)-quasinormally embedded subgroups of finite groups
... Theorem. Let H be a normal subgroup in G, and p a prime divisor of |H | such that (p−1, |H|) = 1. Let P be a Sylow p-subgroup in H. Assume that all maximal subgroups in P are SE-supplemented in G. Then H is ... See full document
8
Finite groups with given $\\sigma$ embedded and $\\sigma$ $n$ embedded subgroups
... We first claim that Q ∩ Φ(G) = 1. In fact, if Q ∩ Φ(G) 6= 1 and let N be a minimal normal subgroup of G contained in Q ∩ Φ(G), then by (7), (G/N, E/N ) satisfies the hypothesis, so G/N ∈ F. Consequently G ∈ F , a ... See full document
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Characterization of finite groups with some \(S\)-quasinormal subgroups of fixed order
... All groups considered in this paper are ...Two subgroups H and K of a group G are said to permute if KH = ...is S-quasinormal in G, if it permutes with every Sylow subgroup of ... See full document
7
On metacyclic subgroups of finite groups
... Over years there has been considerable literature studying global properties of groups which are determined by the structure or embedding of their Sylow p-subgroups, where p is a prime which is going to be ... See full document
5
On finite groups with Hall normally embedded Schmidt subgroups
... Since S is arbitrary, we conclude that all 2-nilpotent Schmidt subgroups of even order are contained in R(G). By Lemma 5, the quotient group G/R(G) has no 2-nilpotent Schmidt subgroups of even order. ... See full document
7
The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups
... is s-permutably embedded in G, where p is the smallest prime dividing |G|, then G is p-nilpotent ([15], Theorem ...of finite groups with the assumption that some maximal subgroups or ... See full document
8
On verbal subgroups in finite and profinite groups
... locally finite and has finite ...locally finite. For abstract groups we have a locally finite version of Schur’s Theorem: if K/Z(K) is locally finite, then K ′ is locally ... See full document
13
Finite groups with semi-subnormal Schmidt subgroups
... A b s t r ac t . A Schmidt group is a non-nilpotent group in which every proper subgroup is nilpotent. A subgroup A of a group G is semi-normal in G if there exists a subgroup B of G such that G = AB and AB 1 is a ... See full document
8
A note on \(c\)-normal subgroups of finite groups
... some prime q and some a, b ∈ N. Assume that G is not p-closed. Then a Sylow q-subgroup Q of G is non-cyclic. Hence by hypothesis, Q has a subgroup D such that 1 < |D| < |Q|, every subroup H satisfying |H| = |D| is ... See full document
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Finite groups whose minimal subgroups are weakly $\mathcal{H}^{\ast}$-subgroups
... Let S be a proper subgroup of G. By Lemma 2.2(a), every cyclic subgroup of S of order p or of order 4 (if p = 2) is a weakly H ∗ -subgroup in ...Thus S satisfies the hypothesis of the theorem and ... See full document
11
Finite non-nilpotent groups with few non-normal non-cyclic subgroups
... the Sylow subgroups of G of odd order are non-normal in G. Thus all of their normalizers are cyclic. By Burnside’s theorem, G has a normal q-complement for each odd prime q ∈ π(G). The intersection of all of these ... See full document
6
Length of the inverse symmetric semigroup
... For groups, it is hard too: the paper [4] uses the classification of finite simple groups to calculate the length of the lattice of subgroups of the symmetric group S n ... See full document
8
On \(p\)-nilpotency of finite group with normally embedded maximal subgroups of some Sylow subgroups
... b s t r a c t . Let G be a finite group and P be a p-subgroup of ...normally embedded in G. Groups with nor- mally embedded maximal subgroups of Sylow p-subgroup, where (|G|, p − ... See full document
8
On finite groups having a certain number of cyclic subgroups
... a finite group and C(G) be the poset of cyclic subgroups of ...the finite group G has | G | − 1 cyclic groups if and only if G is isomorphic to Z 3 , Z 4 , S 3 , or D 8 ... See full document
8
An application of the concept of a generalized central element
... a finite group G is said to be S-quasinormal in G if it permutes with every Sylow subgroup of ...a finite group G is said to be S-quasinormally embedded in G if for each prime p ... See full document
10
\(\mathbf{S}\)-Embedded subgroups in finite groups
... (resp. S- semipermutable) provided that it permutes with every subgroup ...An S-semipermutable subgroup of a group need not be ...and S-semipermutable but not ... See full document
8
Finite groups with some $SS$-embedded subgroups
... all subgroups, independently of whether they are normal, s-permutable, c-normal, nearly s-normal or S-embedded in G are SS-embedded subgroups of ...not ... See full document
8
Partially $S$-embedded minimal subgroups of finite groups
... The fact that p n+1 ||G| follows from Lemma 2.6. Let L be a proper subgroup of G, then (|L|, (p − 1)(p 2 −1) · · · (p n −1)) = 1. If p n+1 - |L|, then Lemma 2.6 implies that L is p-nilpotent. Now we assume that p n+1 ... See full document
10
A note on Hall S-permutably embedded subgroups of finite groups
... A b s t r a c t . Let G be a finite group. Recall that a subgroup A of G is said to permute with a subgroup B if AB = BA. A subgroup A of G is said to be S-quasinormal or S-permutable in G if ... See full document
7
On well \(p\)-embedded subgroups of finite groups
... If A ≤ H, then G/H = BH/H ≃ B/B ∩ H is dispersive. Let now A 6⊆ H. Since |G/H| < |G|, we need to be shown that hypothesis of the theorem is true for G/H. Clearly, G/H = (HA/H)(BH/H), where HA/H is s-quasinormal ... See full document
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