[PDF] Top 20 On some non-periodic groups whose cyclic subgroups are \(GNA\)-subgroups
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On some non-periodic groups whose cyclic subgroups are \(GNA\)-subgroups
... In the same time, there are subgroups that combine the concepts of normality and abnormality. Recall that a subgroup H of a group G is called pronormal in G if for every element g ∈ G the subgroups H and H ... See full document
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On locally finite groups whose cyclic subgroups are \(\mathrm{GNA}\)-subgroups
... (in some sense) to all ...of groups whose subgroups are either P -subgroups or AP -subgroups (for example, normal or abnormal ...(in some sense) version of this ... See full document
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Finite groups whose minimal subgroups are weakly $\mathcal{H}^{\ast}$-subgroups
... every cyclic subgroup of S of order p or of order 4 (if p = 2) is a weakly H ∗ -subgroup in ...minimal non p-nilpotent group (non p-nilpotent group all of its proper subgroups are ...minimal ... See full document
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On Fitting groups whose proper subgroups are solvable
... Proof of Theorem 1.6. Let G be a Fitting p-group satisfying the normalizer condition, where p ̸ = 2. Suppose that G satisfies the hypothesis of the theorem. Assume that G is perfect. As in the proof of Theorem 1.4, we ... See full document
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Groups whose non-normal subgroups have small commutator subgroup
... a periodic abelian group with no ele- ments of order ...of groups for which the set of non-normal subgroups is small in some sense has been studied by many authors in several different ... See full document
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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 ... See full document
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Groups whose proper subgroups of infinite rank have polycyclic-by-finite conjugacy classes
... proper subgroups M and N such that G = M N and G/M and G/N are non-cyclic groups of rank ...a non-perfect group and suppose first that G is a minimal non- (P F ...proper ... See full document
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Non-nilpotent groups with three conjugacy classes of non-normal subgroups
... Now we assume that |L| = q is a prime. Hence P is maximal in M . If L H, then H 6 P, as P is cyclic and normal in M , then H E M . So LH is normal in G and contains H as a characteristic subgroup, hence H E G, a ... See full document
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On groups whose subgroups of infinite special rank are transitively normal
... a cyclic subgroup haci is G-invariant, (ac) g = (ac) m = a m c m for some positive integer m such that 1 < k < ...a periodic soluble group of infinite special rank whose subgroups ... See full document
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Finite groups with some $SS$-embedded subgroups
... M = 1 and G is a cyclic group of prime order. Thus it is soluble, as required. Next, we let N be a minimal normal subgroup of G. Clearly the hypothesis holds for G/N by Lemma 2.2, so by induction we have G/N is ... See full document
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Groups with permutability conditions for subgroups of infinite rank
... permutable subgroups need not to be ...quasihamiltonian groups is well known, we refer to [10] for a detailed ...a non-periodic quasihamiltonian group G the set of all elements of finite order ... See full document
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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) ...a non-trivial cyclic Sylow 2-subgroup is non-sinple and it follows from the Feit-Thonpson Theorem that it is even ... See full document
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Finite groups with semi-subnormal Schmidt subgroups
... All groups in this paper are finite. A Schmidt group is a non-nilpotent group in which every proper subgroup is ...These groups were first considered by ...Sylow subgroups is normal and ... See full document
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On metacyclic subgroups of finite groups
... a cyclic group of order q and let V be an irreducible and faithful C-module over the finite field of ...a non p-supersoluble group with a metacyclic Sylow p-subgroup such that ( | G | , p − 1) = ... See full document
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The groups whose cyclic subgroups are either ascendant or almost self-normalizing
... Proof of Corollary A2. Put B = Gru(G). Then B = P × R, where P is a Sylow p-subgroup of B and R is a Sylow p ′ -subgroup of B. By our conditions R is finite. Consider a factor-group G/R. Suppose that the Sylow p ′ ... See full document
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Locally soluble groups with the restrictions on the generalized norms
... infinite cyclic subgroup has a nonidentity intersection with the norm N G A ...Abelian subgroups of rank ...such subgroups. A similar statement holds for non-cyclic Abelian ... See full document
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On the non–periodic groups, whose subgroups of infinite special rank are transitively normal
... The groups with certain prescribed properties of subgroups form one of the central subjects of research in group ...permutability, some important numerical invariants on groups, in particular, ... See full document
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Generalized norms of groups
... all subgroups of the group G to the system of all Abelian and all cyclic subgroups does not lead to extension of the concept of the norm N ...all non-cyclic subgroups (provided ... See full document
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A characterization of supersolubility of finite groups
... by all those subgroups of H which are S-quasinormal in G. As a generalization and unifi- cation of the above two different kinds of embedding property of subgroups, Li and Chen in [] introduced the concept ... See full document
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On the \(\cal F\) -hypercentre of a finite group
... Following Robinson [22], a group G is said to be an SC-group if every chief factor of G is a simple group. SC-Groups have many interesting properties. In particular, the class of all such groups is a new ... See full document
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