in this article we introduce the notion of n-capable groups. it is shown that every group g admits a uniquely determined subgroup (〖z^n)〗^* (g) which is a characteristic subgroup and lies in the n-centre subgroup of the group g. this is the smallest subgroup of g whose factor group is n-capable. moreover, some properties of n-central extension will be studied.

This paper details the diassociative analogue of results concerning Schur multiplier and other extension-theoretic concepts that originate in group theory. We first prove covers algebras are unique. Second, we show a algebra is characterized by second cohomology with coefficients field. Third, establish criteria for when center cover maps onto algebra. Along way, obtain collection exact sequenc...

In this article we introduce the notion of n-capable groups. It is shown that every group G admits a uniquely determined subgroup (〖Z^n)〗^* (G) which is a characteristic subgroup and lies in the n-centre subgroup of the group G. This is the smallest subgroup of G whose factor group is n-capable. Moreover, some properties of n-central extension will be studied.

Using a new classification of 2-generator p-groups of class 2, we compute various homological functors for these groups. These functors include the nonabelian tensor square, nonabelian exterior square and the Schur multiplier. We also determine which of these groups are capable and which are unicentral.

In this paper, we prove Leibniz analogues of results found in Peggy Batten’s 1993 dissertation. We first construct a Hochschild–Serre-type spectral sequence low dimension, which is used to characterize the multiplier terms second cohomology group with coefficients field. The then extended by term and Ganea constructed for algebras. maps involved these exact sequences, as well characterization m...

 Let $R$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎A right $R$-module $M$ is called $(n‎, ‎d)$-projective if $Ext^{d+1}_R(M‎, ‎A)=0$ for every $n$-copresented right $R$-module $A$‎. ‎$R$ is called right $n$-cocoherent if every $n$-copresented right $R$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $R$-module is $(n‎, ‎d)$-projective‎. ‎$R$...

MNDO semi-empirical SCF MO calculations are used to study the pyramidal nitrogen atom inversion and configurational equilibria in the title compounds.

let $r$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎a right $r$-module $m$ is called $(n‎, ‎d)$-projective if $ext^{d+1}_r(m‎, ‎a)=0$ for every $n$-copresented right $r$-module $a$‎. ‎$r$ is called right $n$-cocoherent if every $n$-copresented right $r$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $r$-module is $(n‎, ‎d)$-projective‎. ‎$r$ ...

mndo semi-empirical scf mo calculations are used to study the pyramidal nitrogen atom inversion and configurational equilibria in the title compounds.

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