Holomorphy of Osborn loops

[1] J. O. Adéníran, On holomorphic theory of a class of left Bol loops, Al.I.Cuza, 51(1), (2005), 23–28Search in Google Scholar

[2] J. O. Adéníran and A. O. Isere, Nuclear Automorphism of a class of Osborn Loops, Journal of the Nigerian Association of Mathematical Physics, 22, (2012), 5-8Search in Google Scholar

[3] J. O. Adéníran, Y. T. Oyebo, and D. Mohammed, On certain isotopic maps of central loops, Proyecciones Journal of Mathematics, 30(3), (2012), 303–31810.4067/S0716-09172011000300003Search in Google Scholar

[4] J. O. Adéníran, T. G. Jaiyéọlá, and K. A. Idowu, Holomorph of generalized Bol loops, Novi Sad Journal of Mathematics, 44 (1), (2014), 37–51Search in Google Scholar

[5] A. S. Basarab, The Osborn loop, Studies in the theory of quasigroups and loops, Shtiintsa, Kishinev, 193, (1973), 12–18Search in Google Scholar

[6] A. S. Basarab, Osborn’s G-loop, Quasigroups and Related Systems, 1(1), (1994), 51–56Search in Google Scholar

[7] A. S. Basarab, Generalised Moufang G-loops, Quasigroups and Related Systems, 3, (1996), 1–6Search in Google Scholar

[8] A. S. Basarab and A.I. Belioglo, UAI Osborn loops, Quasigroups and loops, Mat. Issled., 51, (1979), 8–16Search in Google Scholar

[9] A. S. Basarab and A. I. Belioglo, Univeral automorphic inverse G-loops, Quasigroups and loops, Mat. Issled., 71, (1979), 3–7Search in Google Scholar

[10] R. H. Bruck, Contributions to the theory of loops, Trans. Amer. Math. Soc., 55, (1944), 245–35410.1090/S0002-9947-1946-0017288-3Search in Google Scholar

[11] R. H. Bruck and L. J. Paige, Loops whose inner mappings are automorphisms, The annuals of Mathematics, 63(2), (1956), 308–32310.2307/1969612Search in Google Scholar

[12] O. Chein and D. A. Robinson, An extra law for characterizing Moufang loops, Proc. Amer. Math. Soc., 33, (1972), 29-3210.1090/S0002-9939-1972-0292987-8Search in Google Scholar

[13] V. O. Chiboka, The study of properties and construction of certain finite order G-loops, Ph.D thesis, Obafemi Awolowo University, Ile-Ife, 1990Search in Google Scholar

[14] V. O. Chiboka and A. R. T. Solarin, Holomorphs of conjugacy closed loops, Scientific Annals of Al.I.Cuza. Univ., 37(3), (1991), 277–284Search in Google Scholar

[15] V. O. Chiboka and A. R. T. Solarin, Autotopism characterization of G-loops, Scientific Annals of Al.I.Cuza. Univ., 39(1), (1993), 19–26Search in Google Scholar

[16] P. Csörgő, Extending the structural homomorphism of LCC loops, Comment. Math. Univ. Carolinae, 46(3), (2005), 385–389Search in Google Scholar

[17] P. Csörgő and A. Drápal, Left conjugacy closed loops of nilpotency class 2, Results Math., 47, (2005), 242–26510.1007/BF03323028Search in Google Scholar

[18] A. Drápal, Conjugacy closed loops and their multiplication groups, J. Alg., 272, (2004), 838–85010.1016/j.jalgebra.2003.06.011Search in Google Scholar

[19] A. Drápal, On multiplicatipon groups of left conjugacy closed loops, Comment. Math. Univ. Carolinae, 45, (2004), 223–236Search in Google Scholar

[20] A. Drápal, On left conjugacy closed loops with a nucleus of index two, Abh. Math. Sem. Univ. Hamburg, 74, (2004), 205–22110.1007/BF02941536Search in Google Scholar

[21] A. Drápal, Structural interactions of conjugacy closed loops, Trans. Amer. Math. Soc., 360, (2008), 671–68910.1090/S0002-9947-07-04131-1Search in Google Scholar

[22] A. Drápal, On extraspecial left conjugacy closed loops, J. Alg., 302(2), (2006), 771–79210.1016/j.jalgebra.2006.04.018Search in Google Scholar

[23] E. D. Huthnance Jr., A theory of generalised Moufang loops, Ph.D. thesis, Georgia Institute of Technology, (1968)Search in Google Scholar

[24] A. O. Isere, S. A. Akinleye, and J. O. Adéníran, On Osborn loops of Order 4n, Acta Universitatis Apulensis Maths. Inform. No., 37, (2014), 31–44Search in Google Scholar

[25] A. O. Isere, J. O. Adéníran, and T. G. Jaiyéọlá, Generalized Osborn Loops of Order 4n, Acta Universitatis Apulensis Maths. Inform. No., 43, (2015), 19–31Search in Google Scholar

[26] A. O. Isere, J. O. Adéníran, and T. G. Jaiyéọlá, Classification of Osborn loops of order 4n, Algebras, Groups and Geometries, to appearSearch in Google Scholar

[27] A. O. Isere, J. O. Adéníran, and A. R. T. Solarin, Some examples of finite Osborn loops, Journal of Nigerian Mathematical Society, 31, (2012), 91-106Search in Google Scholar

[28] T. G. Jaiyéọlá, The study of the universality of Osborn loops, Ph.D. thesis, University of Agriculture, 2008 Abeokuta.Search in Google Scholar

[29] T. G. Jaiyéọlá, On Three Cryptographic Identities in Left Universal Osborn Loops, Journal of Discrete Mathematical Science and Cryptography, 14(1), (2011), 33-50 (DOI:10.1080/09720529.2011.10698322)Search in Google Scholar

[30] T. G. Jaiyéọlá, Osborn loops and their universality, Scientific Annals of ”Al.I. Cuza” University of Iasi., Tomul, 58(2), (2012), 437–45210.2478/v10157-012-0018-7Search in Google Scholar

[31] T. G. Jaiyéọlá, New identities in universal Osborn loops II, Algebras, Groups and Geometries, 30(1), (2013), 111–126Search in Google Scholar

[32] T. G. Jaiyéọlá, On Two Cryptographic Identities in Universal Osborn Loops, Journal of Discrete Mathematical Sciences and Cryptography, 16(2-3), (2013), 95-116 (DOI:10.1080/09720529.2013.821371)Search in Google Scholar

[33] T. G. Jaiyéọlá, On some simplicial complexes of universal Osborn loops, Analele Universitatii De Vest Din Timisoara, Seria Matematica-Informatica, 52(1), (2014), 65-79 (DOI: 10.2478/awutm-2014-0005)Search in Google Scholar

[34] T. G. Jaiyéọlá and B. A. Popoola, Holomorph of generalized Bol loops II, Discussiones Mathematicae-General Algebra and Applications, 35(1), (2015), 59-78 (doi:10.7151/dmgaa.1234)Search in Google Scholar

[35] T. G. Jaiyéọlá and J. O. Adéníran, New identities in universal Osborn loops, Quasigroups and Related Systems, Moldova, 179(1), (2009), 55–76Search in Google Scholar

[36] T. G. Jaiyéọlá and J. O. Adéníran, Not Every Osborn loop is universal, Acta Math. Acad. Paed. Nviregvhaziensis, 25, (2009), 189-190Search in Google Scholar

[37] T. G. Jaiyéọlá and J. O. Adéníran, Loops that are isomorphic to their Osborn loop isotopes(G-Osborn loops), Octogon Mathematical Magazine, 19(2), (2011), 328-348Search in Google Scholar

[38] T. G. Jaiyéọlá and J. O. Adéníran, On Another Two Cryptographic Identities In Universal Osborn Loops, Surveys in Mathematics and its Applications, 5, (2010), 17-34Search in Google Scholar

[39] T. G. Jaiyéọlá, J. O. Adéníran, and A. R. T. Sòlárìn, The universality of Osborn loops, Acta Universitatis Apulensis Mathematics-Informatics, 26, (2011), 301-320Search in Google Scholar

[40] T. G. Jaiyéọlá, J. O. Adéníran, and A. R. T. Sòlárìn, Some necessary conditions for the existence of a finite Osborn loop with trivial nucleus, Algebras, Groups and Geometries, 28(4), (2011), 363–380Search in Google Scholar

[41] T. G. Jaiyéọlá, J. O. Adéníran, and A. A. A. Agboọlá, On the second Bryant Schneider group of universal Osborn loops, Societatea Română de Matematică Aplicată si Industrială Journal (ROMAI J.), 9(1), (2013), 37–50Search in Google Scholar

[42] M. K. Kinyon, A survey of Osborn loops, Milehigh conference on loops, quasigroups and non-associative systems, University of Denver, Denver, Colorado, (2005)Search in Google Scholar

[43] M. K. Kinyon and K. Kunen, The structure of extra loops, Quasigroups and Related Systems, 12, (2004), 39–60Search in Google Scholar

[44] M. K. Kinyon and K. Kunen, Power-associative conjugacy closed loops, J. Alg., 304(2), (2006), 679–71110.1016/j.jalgebra.2006.01.034Search in Google Scholar

[45] M. K. Kinyon, K. Kunen, and J. D. Phillips, Diassociativity in conjugacy closed loops, Comm. Alg., 32, (2004), 767–78610.1081/AGB-120027928Search in Google Scholar

[46] M.K. Kinyon, K. Kunen, and J.D. Phillips, A generalisation of Moufang and Steiner loops, Alg. Univer., 48(1), (2002), 81–10110.1007/s00012-002-8205-0Search in Google Scholar

[47] K. Kunen, G-loops and Permutation Groups, J. Alg., 220, (1999), 694–70810.1006/jabr.1999.8006Search in Google Scholar

[48] K. Kunen, The structure of conjugacy closed loops, Trans. Amer. Math. Soc., 352, (2000), 2889–291110.1090/S0002-9947-00-02350-3Search in Google Scholar

[49] J. M. Osborn, A theorem on A-loops, Proc. Amer. Math. Soc., 9, (1959), 347–34910.1090/S0002-9939-1958-0093555-6Search in Google Scholar

[50] J. M. Osborn, Loops with the weak inverse property, Pac. J. Math., 10, (1961), 295–30410.2140/pjm.1960.10.295Search in Google Scholar

[51] H. O. Pflugfelder, Quasigroups and loops : Introduction, Sigma series in Pure Math. 7, Heldermann Verlag, Berlin, 1990Search in Google Scholar

[52] D. A. Robinson, Bol loops, Ph. D thesis, University of Wisconsin, 1964Search in Google Scholar

[53] D. A. Robinson, Holomorphic theory of extra loops, Publ. Math. Debrecen, 18, (1971), 59–6410.5486/PMD.1971.18.1-4.07Search in Google Scholar