Abstract Let $$\Gamma &lt; G$$ Γ &lt; G be a discrete subgroup of locally compact unimodular group G . $$m\in C_b(G)$$ m ∈ C b ( )</mml:m...

Many work was done for filiform Lie algebras defined by M. Vergne [8]. An interesting fact is that this algebras are obtained by deformations of the filiform Lie algebra Ln,m. This was used for classifications in [4]. Like filiform Lie algebras, filiform Lie superalgebras are obtained by nilpotent deformations of the Lie superalgebra Ln,m. In this paper, we recall this fact and we study even co...

In this paper and its sequel we continue our study of nilpotent symplectic alternating algebras. In particular we give a full classification of such algebras of dimension 10 over any field. It is known that symplectic alternating algebras over GF(3) correspond to a special rich class C of 2-Engel 3-groups of exponent 27 and under this correspondance we will see that the nilpotent algebras corre...

Given a nilpotent Lie algebra L of dimension $$\le 6$$ on an arbitrary field characteristic $$\ne 2$$ , we show direct method to detect whether is capable or not via computations the size its nonabelian exterior square $$L \wedge L$$ . For dimensions higher than 6, result general nature, based evidences low dimensional case, but also large families algebras, namely generalized Heisenberg algebr...

for any group g, let c(g) denote the set of centralizers of g.we say that a group g has n centralizers (g is a cn-group) if |c(g)| = n.in this note, we prove that every finite cn-group with n ≤ 21 is soluble andthis estimate is sharp. moreover, we prove that every finite cn-group with|g| < 30n+1519 is non-nilpotent soluble. this result gives a partial answer to aconjecture raised by a. ashrafi in ...

Among other things, we prove that the group of automorphisms fixing every normal subgroup of a (nilpotent of class c)-by-abelian group is (nilpotent of class ≤ c)-by-metabelian. In particular, the group of automorphisms fixing every normal subgroup of a metabelian group is soluble of derived length at most 3. An example shows that this bound cannot be improved.

In the present paper, we study notion of Schur multiplier M(L) an n-Lie superalgebra L=L0?L1 and prove that dim M(L)??i=0n(mi)L(n?i,k), where L0=m, L1=k, L(0,k)=1 L(t,k)=?j=1t(t?1j?1)(kj), for 1?t?n. Moreover, obtain upper bound dimension in which L is a nilpotent with one-dimensional derived superalgebra. It also provided several inequalities on as well analogue converse Schur’s theorem.

For any group G, let C(G) denote the set of centralizers of G.We say that a group G has n centralizers (G is a Cn-group) if |C(G)| = n.In this note, we prove that every finite Cn-group with n ≤ 21 is soluble andthis estimate is sharp. Moreover, we prove that every finite Cn-group with|G| < 30n+1519 is non-nilpotent soluble. This result gives a partial answer to aconjecture raised by A. Ashrafi in ...

We prove that every finitely generated Lie algebra containing a nilpotent ideal of class c and finite codimension n has Gelfand-Kirillov dimension at most cn. In particular, finitely generated virtually nilpotent Lie algebras have polynomial growth.

Let G be a group. An endomorphism φ of G is called rational if there exist a1, . . . , ar ∈ G and h1, . . . , hr ∈ Z, such that φ(x) = (xa1)1 . . . (xar)r for all x ∈ G. We denote by Endr(G) the group of invertible rational endomorphisms of G. In this note, we prove that G is nilpotent of class c (c ≥ 3) if and only if Endr(G) is nilpotent of class c − 1. Mathematics Subject Classification: 20E...