finitely generated nilpotent groups
On verbal subgroups of finitely generated nilpotent groups
... torsion-free finitely generated nilpotent groups is known (see ...a finitely generated torsion-free nilpo- tent group 𝐺 has the lower central series with infinite cyclic ...
10
On almost finitely generated nilpotent groups
... In the category of abelian groups a subgroup of an fg-like group is fg-like, ii an extension of an fg-like group by an fg-like group is fg-like We thus devote much attention to the statu[r] ...
6
A sequence of factorizable subgroups
... of groups with max are finitely generated nilpotent groups and polycyclic ...each finitely generated nilpotent group and polycyclic group has a CF-sequence of ...
10
Commutator Length of Finitely Generated Linear Groups
... Lemma 3.3 Jordan 13. If char F 0, and G is a soluble-by-finite subgroup of GLn, F, then G contains a soluble normal subgroup of finite index at most βn √ 8n 1 2n 2 − √ 8n − 1 2n 2 . Proof of Theorem B. By Tits’s theorem, ...
5
Groups with many pronormal and transitively normal subgroups
... non-finitely generated, is normal in ...locally nilpotent, some hypercenter of G includes T ...non-finitely generated, is ascendant in ...
23
On Semiabelian Groups
... a finitely generated semiabelian ...a nilpotent finitely gen- erated group, its periodic part t(G) is also finitely generated (see, ...is finitely generated, the ...
6
Automorphisms fixing subnormal subgroups of certain infinite soluble groups
... ABELIAN-BY-NILPOTENT GROUPS Recall from Chapter 5 our main result Theorem E, that if G is a finitely generated infinite metabelian group, then the group Autsn G is a finite Abelian group[r] ...
92
Groups with many pronormal and transitively normal subgroups
... index in A. By above remarked, this means that A = A∩C. Moreover, every term of an upper Z(K/A)-central series is a pure G-invariant subgroup. It follows that A = ξ Z(K/A) (A), that is A ≤ ξ(K) and a subgroup K is ...
18
Some aspects of nilpotent groups
... is nilpotent. For example it is proved that, if N is finitely generated, then G is nilpotent although, in this case, no bound on the class of G is ...is nilpotent of class at most end + ...
131
Computing invariants for finitely presented nilpotent groups
... The second problem centres on classifying finitely generated, torsion- free nilpotent groups of class 2 . Canonical presentations can be given for each such group. A skew-symmetric matrix can ...
178
Soluble Lie rings
... Finitely generated abelian by nilpotent groups are residually finite... have been obtained for Lie algebras:.[r] ...
125
On nilpotent Chernikov 2-groups with elementary tops
... If m > 2, a classification of m-tuples of skew-symmetric matrices is a wild problem in the sense of the representation theory, i.e. it contains a classification of representations of any finitely ...
8
Groups with Identical $k$-Profiles
... Proof. Let G,H be two groups of order n. By our assumption, G and H are isomorphic if and only if their k-profiles agree, so we only need to show how to compare the k-profiles of the two groups. This can be ...
7
MoL 2001 09: Finite Projective Formulas
... each finitely gen- erated projective Heyting algebra there corresponds a projective formula; to non-isomorphic finitely generated projective algebras there correspond non- equivalent projective ...
49
A classification of nilpotent $3$-BCI groups
... In Section 2, following the ideas of [3], we will see that the BCI-property of a given bi-Cayley graph can be read off entirely from its automorphism group (see Lemma 2.2). This was observed for cyclic groups in ...
14
Finite p′ nilpotent groups I
... It is well known that p-nilpotent groups form a subgroup closed saturated formation and that the intersection of two subgroup closed saturated formations is a subgroup closed saturated f[r] ...
12
Some properties of nilpotent groups
... A class 𝒱 closed under H, S and P is a variety of groups. The isomorphism class ℰ of the one element group is the trivial variety. All other varieties 𝒱 ∕= ℰ are nontrivial. A classical result of Garrett Birkhoff ...
12
Semigroups with finitely generated universal left congruence
... is finitely gen- erated that lie in certain important classes, such as strong semilattices of semigroups, inverse semigroups, Rees matrix semigroups (over semigroups) and completely regu- lar ...is finitely ...
37
Periodic rings with finitely generated underlying group
... For the rest of the paper, we deal with rings which do not necessarily have identity. Proposition 2.2. Let R be a periodic ring such that (R, +) is finitely generated. Then R fits into an extension F → R → ...
6
Commutators and Squares in Free Nilpotent Groups
... We prove that in the free nilpotent group F2,3 x1 , x2 of rank 2 and class 3 freely generated by x1 , x2 it is possible to write certain nontrivial commutators as a proper power.. We c[r] ...
10