[PDF] Top 20 On inequalities of subgroups and the structure of finite groups
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On inequalities of subgroups and the structure of finite groups
... The authors are grateful to the referees for their helpful suggestions. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11271301, 11171364, 11001226), the Scientific Research ... See full document
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Partially $S$-embedded minimal subgroups of finite groups
... the structure of a finite group is an active topic in the group ...a finite group, ...normal subgroups (see, for example, [1], [2], [4], [9], ... See full document
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Centralizers in simple locally finite groups
... the structure of centralizers of elements in simple locally finite groups gives information about the structure of proper subgroups and internal structure of subgroup lattice of ... See full document
10
Non-nilpotent groups with three conjugacy classes of non-normal subgroups
... non-normal subgroups of ...classified finite groups with ν(G) = ...the structure of finite groups, so many authors work on this concept but mostly in ... See full document
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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 ...SS-embedded subgroups on the structure of a ... See full document
8
Finite groups with cyclic Sylow subgroups for all odd primes
... the structure of G^, if n o n - s o l u b l e , is completely ...only groups G , which are non-soluble and have our property, are, modulo odd order normal subgroups, isomorphic to S(p), for some ... See full document
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On metacyclic subgroups of finite groups
... 2-generator subgroups on the structure of a ...2-generator subgroups in a class X of groups which is subgroup-closed and the minimal non-X-groups are ... See full document
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On finite groups having a certain number of cyclic subgroups
... a finite group and C(G) be the poset of cyclic subgroups of ...the structure of C(G) has an influence on the algebraic structure of ...the finite group G has | G | − 1 cyclic ... See full document
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Finite groups whose minimal subgroups are weakly $\mathcal{H}^{\ast}$-subgroups
... the structure of 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 ... See full document
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Structure of Groups with Generalized Normal Subgroups
... has finite many normalizers of infinite subgroups which are neither almost normal nor nearly ...infinite subgroups are almost normal or all infinite subgroups of G are nearly ...is ... See full document
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Subnormal Structure of Finite Soluble Groups
... A- groups, nilpotent groups, metabelian groups, abelian-by-nilpotent groups and, more generally, groups of p-length 1 for all p; in particular any such group G satisfies wl(G) 6 2 · wl ... See full document
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Finite non-nilpotent groups with few non-normal non-cyclic subgroups
... non-cyclic subgroups of Q is normal in G, so S ⩽̸ Q is non-abelian, then G ′ = S ′ , and S ⊴ G; a ...quaternion structure, then Q ∩ M = Φ(Q) and all the maximal subgroups of Q are non-normal in ... See full document
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On free subgroups of finite exponent in circle groups of free nilpotent algebras
... multiplicative structure into the structure with respect to ∗ , we know that ⟨ X ⟩ ∗ as a subgroup of the algebra of power series is a free group, freely generated by ... See full document
12
The number of maximal subgroups and probabilistic generation of finite groups
... Here the symbol ⌊ x ⌋ is used to denote the defect integer part of x, that is, the largest integer number n with n ≤ x. The proof of this result depends on some results of Dalla Volta and Lucchini [6] and Dalla Volta, ... See full document
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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 of G containing H. A ... See full document
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Near Frattini subgroups of residually finite generalized free products of groups
... An element g of a group G is a near generator of G if there exists a subset S of G such that |G : S| is infinite, but |G : g,S| is finite. Thus, an element g of G is a non-near generator of G if for every subset S of G, ... See full document
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Minimal conditions on Clifford semigroup congruences
... If X is a nonempty subset of a group G, the normal closure of X in G, denoted by X G , is the intersection of all normal subgroups of G which contains X. Dually, the core of X in G, denoted by X G , is the join of ... See full document
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Groups whose proper subgroups of infinite rank have polycyclic-by-finite conjugacy classes
... non-trivial finite or abelian factor ...are finite cyclic extensions of divisible abelian p-groups of finite rank, where p is a prime, hence they are Chernikov ...for groups having a ... See full document
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Finite simple groups which are the products of symmetric or alternating groups with $L_{3}(4)$
... simple groups for which the factors are maximal subgroups have been determined in ...all finite groups G = AB are found where A is a non-abelian simple group and B is isomorphic to A 5 ...all ... See full document
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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
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