Academic Journal
Nonsplitting F-quasigroups
| العنوان: | Nonsplitting F-quasigroups |
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| المؤلفون: | Gagola III, Stephen |
| بيانات النشر: | Charles University in Prague, Faculty of Mathematics and Physics |
| سنة النشر: | 2012 |
| المجموعة: | DML-CZ (Czech Digital Mathematics Library) |
| مصطلحات موضوعية: | keyword:F-quasigroup, keyword:NK-loop, keyword:Moufang loop, msc:20E10, msc:20N05 |
| الوصف: | summary:T. Kepka, M.K. Kinyon and J.D. Phillips: The structure of F-quasigroups, J. Algebra 317 (2007), no. 2, 435--461 developed a connection between F-quasigroups and NK-loops. Since NK-loops are contained in the variety generated by groups and commutative Moufang loops, a question that arises is whether or not there exists a nonsplit NK-loop and likewise a nonsplit F-quasigroup. Here we prove that there do indeed exist nonsplit F-quasigroups and show that there are exactly four corresponding nonsplit NK-loops of minimal order $3^6$. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 0010-2628 1213-7243 |
| Relation: | mr:MR3017836; zbl:Zbl 1257.20068; reference:[1] Belousov V.D.: About one quasigroup class.Uchenye Zapiski Beltskogo Gospedinstituta im. A. Russo, \bf 5 \rm (1960), 29–44 (in Russian).; reference:[2] Bol G.: Gewebe und Gruppen.Math. Ann. 114 (1937), no. 1, 414–431. Zbl 0016.22603, MR 1513147, 10.1007/BF01594185; reference:[3] Bruck R.H.: A Survey of Binary Systems.Springer, New York, 1971. Zbl 0141.01401, MR 0093552; reference:[4] Gagola S.M. III: A Moufang loop's commutant.Proc. Cambridge Phil. Soc. 152 (2012), no. 2, 193–206. MR 2887872; reference:[5] Gagola S.M. III: The number of Sylow $p$-subloops in finite Moufang loops.Comm. Algebra 38 (2010), no. 4, 1436–1448. MR 2656586, 10.1080/00927870902950647; reference:[6] Kepka T., Bénéteau L., Lacaze J.: Small finite trimedial quasigroups.Comm. Algebra 14 (1986), no. 6, 1067–1090. Zbl 0606.20061, MR 0837271, 10.1080/00927878608823353; reference:[7] Kepka T., Kinyon M.K., Phillips J.D.: F-quasigroups and generalized modules.Comment. Math. Univ. Carolin. 49 (2008), no. 2, 249–257. MR 2426889; reference:[8] Kepka T., Kinyon M.K., Phillips J.D.: The structure of F-quasigroups.J. Algebra 317 (2007), no. 2, 435–461. Zbl 1133.20051, MR 2362925, 10.1016/j.jalgebra.2007.05.007; reference:[9] Kepka T., Němec P.: Commutative Moufang loops and distributive groupoids of small orders.Czechoslovak Math. J. 31 (106) (1981), no. 4, 633–669. Zbl 0573.20065, MR 0631607; reference:[10] Murdoch D.C.: Quasi-groups which satisfy certain generalized associative laws.Amer. J. Math. 61 (1939), 509–522. Zbl 0020.34702, MR 1507391, 10.2307/2371517; reference:[11] Pflugfelder H.O.: Quasigroups and Loops: Introduction.Sigma Series in Pure Mathematics, 7, Heldermann, Berlin, 1990. Zbl 0715.20043, MR 1125767 |
| الاتاحة: | http://hdl.handle.net/10338.dmlcz/142930 |
| Rights: | access:Unrestricted ; rights:DML-CZ Czech Digital Mathematics Library, http://dml.cz/ ; rights:Institute of Mathematics AS CR, http://www.math.cas.cz/ ; conditionOfUse:http://dml.cz/use |
| رقم الانضمام: | edsbas.59664A17 |
| قاعدة البيانات: | BASE |
| تدمد: | 00102628 12137243 |
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