[PDF] Top 20 Cyclic permutable subgroups of finite groups
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Cyclic permutable subgroups of finite groups
... It follows from Theorem 1.1 and [9, Theorem 2.3.1] that in a finite group the normal closure of a cyclic permutable subgroup of odd order is a modular group, giving a positive answer to [r] ... See full document
9
Finite groups with given $\\sigma$ embedded and $\\sigma$ $n$ embedded subgroups
... of H which are s-permutable in G (note that a subgroup A of G is said to be s-permutable in G if AP = P A for any Sylow subgroup P of G) and H sG the intersection of all s-permutable subgroups ... See full document
20
Model subgroups of finite soluble groups
... Proof. We can assume that C / 1. So C contains an element o f prime order, which induces a fixed point free automorphism o f prime order on N . So N is nilpotent by Theorem 1.7.6. Let Q be a p-Sylow subgroup o f the ... See full document
186
On inequalities of subgroups and the structure of finite groups
... Let L be a proper subgroup of G. Because L/L ∩ N LN/N ≤ G/N and G/N is p- nilpotent, L/L ∩ N is p-nilpotent. By the hypothesis and Lemma ., every cyclic subgroup of L ∩ N with order (if p=) is weakly ... See full document
7
A characterization of supersolubility of finite groups
... Let G be a group and H be a subgroup of G. H is said to be a permutable (or quasi- normal) subgroup of G if H permutes with every subgroup of G. If H permutes with ev- ery Sylow subgroup of G, then we call H an ... See full document
6
Finite groups with some $SS$-embedded subgroups
... All groups considered in this paper are finite and G denotes a group, H E E G means that H is a subnormal subgroup of ...a finite group is a common method in the study of group ...is ... See full document
8
On metacyclic subgroups of finite groups
... Example 10. Let p, q be two primes such that 2 < q divides p + 1. Let C be a cyclic group of order q and let V be an irreducible and faithful C-module over the finite field of p-elements. Then V is an ... See full document
5
Finite groups whose minimal subgroups are weakly $\mathcal{H}^{\ast}$-subgroups
... a finite group G under the assumption that the minimal subgroups of G and the cyclic subgroups of order 4 satisfying one of the previously mentioned concepts (recall that a minimal subgroup of ... See full document
11
Product of pairwise permutable nilpotent n subgroups A1,…,At.
... factorized groups. He proved that every product of two abelian groups is ...of cyclic groups, and around 1965 ...locally finite factorized ... See full document
5
Partially $S$-embedded minimal subgroups of finite groups
... From minimal subgroup’s generalized normalities to characterize the structure of a finite group is an active topic in the group theory. For example, Buckley and Itˆ o have got some well-known results about the ... See full document
10
The embedding of a cyclic permutable subgroup in a finite group II
... a cyclic permutable subgroup A = a of a finite 2-group G and B = [A, G, ...each cyclic subgroup of B has the form [u, a] = K, say, for some element u in [A, ... See full document
10
Groups with all subgroups permutable or soluble
... in groups in which only certain subgroups have some given property and a common theme has been to consider groups whose normal (or subnormal or permutable) subgroups are abelian (or ... See full document
7
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
Finite groups with cyclic Sylow subgroups for all odd primes
... a cyclic 2-group is itself a cyclic 2-group, we see that N(S) = C(S) ...non-trivial cyclic Sylow 2-subgroup is non-sinple and it follows from the Feit-Thonpson Theorem that it is even ...to ... See full document
115
Finite non-nilpotent groups with few non-normal non-cyclic subgroups
... and both of them have q conjugates in QK. Therefore q is odd and QK contains q(q + 1) subgroups isomorphic to HK all of which are conjugate in G. Since HK has q | M : K | conjugate in G, then | M : K | = q + 1 and ... See full document
6
On the semi cover-avoiding property and $\mathcal{F}$-supplementation
... solvable groups, later by Gillam (see [6]) and Ezquerro (see [3]), et ...certain subgroups of G have the semi cover-avoiding property (see [9] and ...some subgroups of Sylow subgroup have the semi ... See full document
11
On free subgroups of finite exponent in circle groups of free nilpotent algebras
... of groups. Furthermore, in case of a finite set X, all the elements in this group have a unique representation in terms of basic ...of groups and provide some ... See full document
12
The number of maximal subgroups and probabilistic generation of finite groups
... With the help of Theorem 2.2 and the precrown associated to a supplemented chief factor and a maximal subgroup supplementing it, studied in [3, Section 1.2], we can prove the following result. Theorem A ([2, Theorem B]). ... See full document
12
Finite groups with all maximal subgroups of prime or prime square index
... -It now follows that whenever G/G is a subdirect product of primitive solvable groups on a prime or prime square number of letters or if G/G} is any homomorphic image of such a group the[r] ... See full document
46
Centralizers in simple locally finite groups
... locally finite groups gives information about the structure of proper subgroups and internal structure of subgroup lattice of the ...non-℘ groups one needs to understand whether such a group ... See full document
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