A-perfect lattice

Abstract

In the Paper [3] authors define the concept of $A$-perfect Group. Inspired by [3], we give a new concept of $A$-perfect lattice. If $g \in L$ and $\alpha \in A$, then the element $[g ; \alpha]=g^{-1} \alpha(g)$ is an auto commutator of $g$ and $\alpha$, if is taken to be an inner automorphism, then the autocommutator sublattice is the derived sublattice $L^{\prime}$ of $L$. A lattice $L$ is said to be perfect if $L=L^{\prime}$. Here, the perception of A-perfect lattices would be introduced. A lattice $L$ would be known as $A$-perfect, if $L=K(L)$.