New structure of algebras using permutations in symmetric groups

The permutation BG-algebras were first introduced as a novel kind of algebra. In this work, their basic qualities were investigated to better understand how they relate to one another and how they might be combined to construct various sorts of superstructures. subalgebra, and permutation BG-normal. Furthermore, we explored certain novel concepts in permutation theory for the initial time. We additionally looked into BG-algebra isomorphism Subject Classification: Primary 20G05, 18A05, Secondary 20D06.