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Keywords:
Bol; Moufang; loop; commutant; associator
Bol; Moufang; loop; commutant; associator
Summary:
Commutative Moufang loops were amongst the first (nonassociative) loops to be investigated; a great deal is known about their structure. More generally, the interplay of commutativity and associativity in (not necessarily commutative) Moufang loops is well known, e.g., the many associator identities and inner mapping identities involving commutant elements, especially those involving the exponent three. Here, we investigate all of this in the variety of Bol loops.
References:
[1] Bruck R.H.: A Survey of Binary Systems. Springer, Berlin-Göttingen-Heidelberg, 1971. MR 0093552 | Zbl 0141.01401
[2] Florja I.A.: Loops with one-sided invertibility. Bul. Akad. Štiince RSS Moldoven (1965), no. 7, 68–79. MR 0197613
[3] Kinyon M.K., Phillips J.D.: Commutants of Bol loops of odd order. Proc. Amer. Math. Soc. 132 (2004), no. 3, 617–619. DOI 10.1090/S0002-9939-03-07211-3 | MR 2019935 | Zbl 1044.20041
[4] McCune W.W.: Prover9 $3.3$ Reference Manual and Guide. Argonne National Laboratory Technical Memorandum ANL/MCS-TM-263, 2003; http://www.mcs.anl.gov/AR/Prover9/
[5] McCune W.W.: Mace $4.0$ Reference Manual and Guide. Argonne National Laboratory Technical Memorandum ANL/MCS-TM-264, 2003; http://www.mcs.anl.gov/AR/mace4/
[6] McCune W.W., Padmanabhan R.: Automated Deduction in Equational Logic and Cubic Curves. Springer, Berlin, 1996. MR 1439047 | Zbl 0921.03011
[7] Phillips J.D.: The Moufang laws, global and local. J. Algebra Appl. 8 (2009), no. 4, 477–492. DOI 10.1142/S021949880900345X | MR 2555515 | Zbl 1190.20052
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