Some Characterizations of Generalized Middle Bol Loops

In this work, the two identities that characterize middle Bol loop (MBL) were separately generalized to define generalized middle Bol loops (GMBL1 and GMBL2) and their relationship was unraveled for possible equivalence. Thereafter, autotopic characterizations of identities GMBL1 and GMBL2 in a loop were carried out. Banking on these, the Bryant-Schneider group characterization of generalized middle Bol loop was carried out. Furthermore, an autotopic-split and right (left) pseudoautomorphic characterization of generalized middle Bol loop were carried out. Furthermore, a right (left) pseudo-automorphic characterization of the isotopy-isomorphy of generalized middle Bol loop was also carried out. This is a sort of "G-generalized middle Bol loop" characterization based on pseudo-automorphic companionship of elements of GMBL as already established for "G-loops".