arXiv:1501.04620v1 [math.GR] 17 Jan 2015 Holomorph of generalized Bol loops ∗† J. O. Ad´ en´ ıran Department of Mathematics, Federal University of Agriculture, Abeokuta 110101, Nigeria. ekenedilichineke@yahoo.com adeniranoj@unaab.edu.ng T. G. Jaiy´ eo . l´ a ‡ Department of Mathematics, Obafemi Awolowo University, Ile Ife 220005, Nigeria. jaiyeolatemitope@yahoo.com tjayeola@oauife.edu.ng K. A. ` Id` ow´ u Department of Mathematics, Federal University of Agriculture, Abeokuta 110101, Nigeria. idowuka@hotmail.com On the 50 th Anniversary of Obafemi Awolowo University Abstract The notion of the holomorph of a generalized Bol loop and generalized flexible-Bol loop are characterized. With the aid of two self-mappings on the holomorph of a loop, it is shown that: the loop is a generalized Bol loop if and only if its holomorph is a gen- eralized Bol loop; the loop is a generalized flexible-Bol loop if and only if its holomorph is a generalized flexible-Bol loop. Furthermore, elements of the Bryant Schneider group of a generalized Bol loop are characterized in terms of pseudo-automorphism, and the automorphisms gotten are used to build the holomorph of the generalized Bol loop. 1 Introduction The birth of Bol loops can be traced back to Gerrit Bol [9] in 1937 when he established the relationship between Bol loops and Moufang loops, the latter which was discovered by Ruth Moufang [26]. Thereafter, a theory of Bol loops evolved through the Ph.D. thesis of * 2010 Mathematics Subject Classification. Primary 20N02, 20NO5 † Keywords and Phrases : generalized Bol loop, flexibility, holomorph of a loop, Bryant Schneider group, pseudo-automorphism ‡ corresponding author 1