\(\sigma\)-nilpotent group
Lie Nilpotent Group Algebras: A Survey
... classified group algebras KG which are strongly Lie nilpotent of index 9, 10, 11, 12 and ...Lie nilpotent group algebras with nilpotency index ...that group algebras with t L (KG) ≤ 6, ...
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On verbal subgroups of finitely generated nilpotent groups
... The characterization of verbal subgroups in a group is an interesting and difficult problem. The full description of the verbal structure has been found only for few specific kinds of groups. The examples are ...
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On finite groups with Hall normally embedded Schmidt subgroups
... p-closed group is a group with a normal Sylow p-subgroup, and a p-nilpotent group is a group of order p a m, where p does not divide m, with a normal subgroup of order ...a group ...
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On hypercentral fyzzy groups
... Fuzzy group theory, as well as other fuzzy algebraic structures, was introduced very soon after the beginning of fuzzy set ...fuzzy group, defined on ...fuzzy group on G based on its algebraic ...in ...
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A new characterization of groups with central chief factors
... A result due to Gruenberg states that a finitely generated torsion free nilpotent group is a residually finite 𝑝-group for every prime 𝑝. See [4] - 5.2.21. We use property (X) to prove an extension ...
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(c,1,...,1) Polynilpotent Multiplier of some Nilpotent Products of Groups
... In this paper we determine the structure of (c, 1, . . . , 1) polynilpotent multiplier of certain class of groups. The method is based on the character- izing an explicit structure for the Baer invariant of a free ...
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Groups with Identical $k$-Profiles
... a nilpotent group G is of class 2 if G 0 ≤ Z(G), where G 0 denotes the commutator subgroup G 0 = [G,G] and Z(G) denotes the center of ...free group with m generators by factoring out all elements u p ...
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On decomposable pseudofree groups
... Abelian group, then N has a trivial Mislin ...generated nilpotent group N as the set of isomorphism classes of (not necessarily finitely generated) nilpotent groups M such that M p N p for all ...
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Finite groups with semi-subnormal Schmidt subgroups
... Schmidt group is a non-nilpotent group in which every proper subgroup is ...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 proper subgroup of G ...
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Groups whose word problems are not semilinear
... generated group and WP ( G ) is the formal language of words defining the identity in ...virtually nilpotent group that is not virtually abelian, the fundamental group of a finite volume ...
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Automorphism groups of metacyclic groups of class two
... in group theory that will be used in the following ...automorphism group of non-split metacyclic p-group of class two, some basic results of the automorphism groups, nilpotent group of ...
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On free subgroups of finite exponent in circle groups of free nilpotent algebras
... Abstract. Let K be a commutative ring with identity and N the free nilpotent K-algebra on a non- empty set X. Then N is a group with respect to the circle composition. We prove that the subgroup generated ...
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Some aspects of nilpotent groups
... a nilpotent group more can be said about the situation of the Frattini subgroup of ...a nilpotent group is normal^ of prime index and contains the derived ...
131
NILPOTENCY AND SOLUBILITY OF GROUPS RELATIVE TO AN AUTOMORPHISM
... a group G, the normal series {1} = Z 0 α (G) E Z 1 α (G) E Z 2 α (G) E · · · is called an upper central α-series and G = Γ α 1 (G) D Γ α 2 (G) D · · · is a lower central α-series for ...
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A sequence of factorizable subgroups
... The most well known classes of groups with max are finitely generated nilpotent groups and polycyclic groups. Therefore, using Theorem 1 and Corollary 1, each finitely generated nilpotent group and ...
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A nilpotent non abelian group code
... find a group G of order 2 6 and an ideal C E F 3 G that is not an abelian group code. Again all smaller p-groups G admit an abelian decomposition, so this is the smallest possible example for non abelian ...
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Finite groups admitting a dihedral group of automorphisms
... the nilpotent group ...Frobenius group with kernel F and complement ...Frobenius-like group in [8] as a generalization of Frobenius group and investigated the structure of G when the ...
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On locally finite groups whose cyclic subgroups are \(\mathrm{GNA}\)-subgroups
... The investigation of influence of some systems of subgroups on the structure of the group is one of the classical problem in group theory. For example, normal subgroups and their natural generalizations ...
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On normalizers in fuzzy groups
... Let γ be the fuzzy group on G, µ be a fuzzy set of G and suppose that µ ⊆ γ. Recall that a fuzzy subgroup, generated by µ is an intersection of all fuzzy subgroups, including µ. We denote this subgroup by < µ ...
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Random walks on finite groups converging after finite number of steps
... A map ϕ : F → f = P g F (g)g is an isomorphism of this algebra on the group algebra RG. We denote functions from F (G) by capital letters and their ϕ-images by corresponding small letters: if F ∈ F(G), then ϕ(F ) ...
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