Nilpotent group
Lie Nilpotent Group Algebras: A Survey
... Lie nilpotent group algebras whose Lie nilpotency indices are next lower, namely 2p and 3p − 1 for p ≥ ...classifying group algebras which are Lie nilpotent having Lie nilpotency indices 2p, ...
8
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 ...
12
On finite groups with Hall normally embedded Schmidt subgroups
... A Schmidt group is a non-nilpotent group in which every proper subgroup is nilpotent. O. Y. Schmidt [3] initiated the investigations of such groups. He proved that a Schmidt group is ...
7
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 ...
7
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
On verbal subgroups of finitely generated nilpotent groups
... Abstract. The paper concerns the problem of characteriza- tion of verbal subgroups in finitely generated nilpotent groups. We introduce the notion of verbal poverty and show that every verbally poor finitely ...
10
(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 ...
13
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 ...
10
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 ...
7
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 ...
12
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 ...
11
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 ...
7
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 ...
6
Finite groups with semi-subnormal Schmidt subgroups
... Schmidt group is a non-nilpotent group in which every proper subgroup is ...Schmidt group is biprimary, one of its Sylow subgroups is normal and another one is ...
8
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 ...
15
NILPOTENCY AND SOLUBILITY OF GROUPS RELATIVE TO AN AUTOMORPHISM
... Let us prove (iii) by assuming (ii). By induction and Lemma 3.7, it can be readily observed that Γ α r−i (G) ≤ Z i α (G), 0 ≤ i ≤ r − 1. Now for i = r − 1 we conclude G = Γ α 1 (G) ≤ Z r−1 α (G) and G = Z r−1 α (G). Thus ...
13
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 ...
17
On normalizers in fuzzy groups
... The above arguments shows that if γ satisfies a normalizer condition, then every fuzzy subgroup of γ is ascendant. We can obtain now a following characterization of fuzzy group satisfying a normalizer condition. ...
14
On locally finite groups whose cyclic subgroups are \(\mathrm{GNA}\)-subgroups
... Lemma 5. Let G be a locally finite group. If every cyclic subgroup of G is a GNA-subgroup, then the derived subgroup [G, G] is locally nilpotent. Proof. Indeed, by Corollary 7, G is locally supersoluble. In ...
12
The influence of nilpotent subgroups on the nilpotent length and derived length of a finite group
... above, nilpotent injectors and Carter subgroups are duals of one ...with nilpotent injectors in place of Carter ...the nilpotent length of a finite soluble group is bounded in terms of the ...
143