[PDF] Top 20 \(\mathbf{S}\)-Embedded subgroups in finite groups
Has 10000 "\(\mathbf{S}\)-Embedded subgroups in finite groups" found on our website. Below are the top 20 most common "\(\mathbf{S}\)-Embedded subgroups in finite groups".
\(\mathbf{S}\)-Embedded subgroups in finite groups
... (2) Let H be a seminormal subgroup of K and K a seminormal subgroup of G. For all primes p ∈ ρ with (|H|, p) = 1 and a Sylow p-subgroup P , there is a Hall ρ-subgroup M of H such that [M, P ] = 1. The theory of certain ... 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
20
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
On verbal subgroups in finite and profinite groups
... b s t r ac t ...many subgroups with a prescribed property, then the verbal subgroup w(G) has the same property as ...the subgroups are periodic or of finite ... 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
11
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
... maximal subgroups of Sylow subgroups of a group ...Subsequently, groups with restrictions on subgroups of M(G) have been studied in the works of many authors, see the literature in ... 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
Partially $S$-embedded minimal subgroups of finite groups
... some subgroups of G satisfy the S-embedded property, many meaningful results have been derived (see [8], [10] ...the s-permutable subgroup, following Chen in [3], a subgroup H of a group G is ... See full document
10
On \(S\)-quasinormally embedded subgroups of finite groups
... b s t r ac t . Let G be a finite group. A subgroup A is called: 1) S-quasinormal in G if A is permutable with all Sylow subgroups in G 2) S-quasinormally embedded in G if every ... See full document
8
A note on Hall S-permutably embedded subgroups of finite groups
... is supersoluble. In particular, X/(N ∩ X) is soluble. Let H be a subgroup of G such that H/(N ∩ X) is a Hall π-subgroup of X/N ∩ X. Suppose that N H is a proper subgroup of G. Then by Lemma 5(1) the hypothesis of the ... See full document
7
Finite groups with some $SS$-embedded subgroups
... By Lemma 2.2(2), we know the hypothesis of the theorem holds for G/N . By the minimal choice of G, we have G/N is p-nilpotent. Since the class of all p-nilpotent groups formed a saturated formation, N is a unique ... See full document
8
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 well \(p\)-embedded subgroups of finite groups
... maximal subgroups of G satisfy (∗) (in this regard, also see the article of Baer ...the subgroups satisfying (∗) were called c-normal in ...c-normal subgroups was presented and some of its ... See full document
15
On supersolvability of finite groups with $\Bbb P$-subnormal subgroups
... Lemma 2.2. Let F be a saturated formation and let G be a solvable group. Assume that G does not belong to F, but G/K ∈ F for all nontrivial normal subgroups K of G. Then G is a primitive group. Proof. First assume ... See full document
9
Related subjects