Abstract
The aim of this paper is the characterization of algebraic properties of Leavitt path algebra of the directed power graph [Formula: see text] and also of the directed punctured power graph [Formula: see text] of a finite group [Formula: see text]. We show that Leavitt path algebra of the power graph [Formula: see text] of finite group [Formula: see text] over a field [Formula: see text] is simple if and only if [Formula: see text] is a direct sum of finitely many cyclic groups of order 2. Finally, we prove that the Leavitt path algebra [Formula: see text] is a prime ring if and only if [Formula: see text] is either cyclic [Formula: see text]-group or generalized quaternion [Formula: see text]-group.
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