A certain algebraic structure of bipolar single value neutrosophic subgroups and its essential properties

The idea of bipolar single value neutrosophic set was created as an extension of a single value neutrosophic set when every single value neutrosophic membership function has two poles. In this study, we apply this idea in an algebraic environment when we initiate the novel concept of bipolar single value neutrosophic subgroups and prove that every bipolar single value neutrosophic subgroup generates two bipolar single value neutrosophic subgroups. we explain the level set, support, kernel for bipolar single value neutrosophic set, bipolar single value neutrosophic characteristic function, and bipolar single value neutrosophic point. Then, we illuminate the bipolar single value neutrosophic subgroup, bipolar single value neutrosophic normal subgroup, bipolar single value neutrosophic conjugate, normalizer for bipolar single value neutrosophic subgroup, bipolar single value neutrosophic abelian subgroup, and bipolar single value neutrosophic factor group. Furthermore, we present the linked theorems and examples and prove these theorems. Finally, we discussed the image and pre-image of bipolar single-value neutrosophic subgroups under homomorphism and proved the related theorems.