We study the notion of Schur multiplier a pair (N, L) Lie superalgebras and obtain some upper bounds concerning dimensions. Moreover, we characterize pairs finite dimensional (nilpotent) for whichfor t = 0; 1, where dim N (m|n).

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.

It is known that the dimension of Schur multiplier a non-abelian nilpotent Lie algebra L n equal to 1 2 (n − 1)(n 2) + s(L) for some ≥ 0. The structure all algebras has been given ≤ 4 in several

‎let $g$ be a finite $p$-group and $n$ be a normal subgroup of $g$ with‎ ‎$|n|=p^n$ and $|g/n|=p^m$‎. ‎a result of ellis (1998) shows‎ ‎that the order of the schur multiplier of such a pair $(g,n)$ of finite $p$-groups is bounded‎ ‎by $ p^{frac{1}{2}n(2m+n-1)}$ and hence it is equal to $‎ ‎p^{frac{1}{2}n(2m+n-1)-t}$ for some non-negative integer $t$‎. ‎recently‎, ‎the authors have characterized...

‎let $g$ be a finite $p$-group and $n$ be a normal subgroup of $g$ with‎ ‎$|n|=p^n$ and $|g/n|=p^m$‎. ‎a result of ellis (1998) shows‎ ‎that the order of the schur multiplier of such a pair $(g,n)$ of finite $p$-groups is bounded‎ ‎by $ p^{frac{1}{2}n(2m+n-1)}$ and hence it is equal to $‎ ‎p^{frac{1}{2}n(2m+n-1)-t}$ for some non-negative integer $t$‎. ‎recently‎, ‎the authors have characterized...

An improvement of a bound of Yankosky (2003) is presented in this paper, thanks to a restriction which has been recently obtained by the authors on the Schur multiplier M(L) of a finite dimensional nilpotent Lie algebra L. It is also described the structure of all nilpotent Lie algebras such that the bound is attained. An important role is played by the presence of a derived subalgebra of maxim...

The McKay–Navarro conjecture is a refinement of the McKay that additionally takes action some Galois automorphisms into account. We verify inductive condition in defining characteristic for finite groups Lie type with exceptional graph automorphisms, Suzuki and Ree groups, Bn(2) (n?2), non-generic Schur multiplier. This completes verification their characteristic.

for a ∈ mn, the schur multiplier of a is defined as s a(x) =a ◦ x for all x ∈ mn and the spectral norm of s a can be stateas ∥s a∥ = supx,0 ∥a ∥x ◦x ∥ ∥. the other norm on s a can be definedas ∥s a∥ω = supx,0 ω(ω s( ax (x ) )) = supx,0 ωω (a (x ◦x ) ), where ω(a) standsfor the numerical radius of a. in this paper, we focus on therelation between the norm of schur multiplier of product of matric...