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.

The non-split extension group $overline{G} = 5^3{^.}L(3,5)$ is a subgroup of order 46500000 and of index 1113229656 in Ly. The group $overline{G}$ in turn has L(3,5) and $5^2{:}2.A_5$ as inertia factors. The group $5^2{:}2.A_5$ is of order 3 000 and is of index 124 in L(3,5). The aim of this paper is to compute the Fischer-Clifford matrices of $overline{G}$, which together with associated parti...

‎in [u‎. ‎dempwolff‎, ‎on extensions of elementary abelian groups of order $2^{5}$ by $gl(5,2)$‎, ‎textit{rend‎. ‎sem‎. ‎mat‎. ‎univ‎. ‎padova}‎, ‎textbf{48} (1972)‎, ‎359‎ - ‎364.] dempwolff proved the existence of a group of the‎ ‎form $2^{5}{^{cdot}}gl(5,2)$ (a non split extension of the‎ ‎elementary abelian group $2^{5}$ by the general linear group‎ ‎$gl(5,2)$)‎. ‎this group is the second l...

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.

If a finite group G has a presentation with d generators and r relations, it is well-known that r−d is at least the rank of the Schur multiplier of G; a presentation is called efficient if equality holds. There is an analogous definition for proficient profinite presentations. We show that many perfect groups have proficient presentations. Moreover, we prove that infinitely many alternating gro...