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A class of finite simple Bol loops of exponent 2
Author(s):
Gábor
P.
Nagy
Journal:
Trans. Amer. Math. Soc.
361
(2009),
5331-5343.
MSC (2000):
Primary 20N05;
Secondary 20C20, 20F29
Posted:
May 28, 2009
MathSciNet review:
2515813
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Abstract:
In this paper we give an infinite class of finite simple right Bol loops of exponent 2. The right multiplication group of these loops is an extension of an elementary Abelian  -group by  . The construction uses the description of the structure of such loops given by M. Aschbacher (2005). These results answer some questions of M. Aschbacher.
References:
-
- 1.
- J. L. ALPERIN. Local representation theory. Cambridge University Press, New York, 1993. MR 860771 (87i:20002)
- 2.
- M. ASCHBACHER. Finite group theory. Cambridge Studies in Advanced Mathematics, 10. Cambridge University Press, Cambridge, 1986. MR 895134 (89b:20001)
- 3.
- M. ASCHBACHER. On Bol loops of exponent 2. J. Algebra 288, No. 1, 99-136 (2005). MR 2138373 (2006k:20131)
- 4.
- M. ASCHBACHER, M. K. KINYON and J. D. PHILLIPS. Finite Bruck loops. Trans. Am. Math. Soc. 358, No. 7, 3061-3075 (2005). MR 2216258 (2006m:20111)
- 5.
- B. BAUMEISTER and A. STEIN. Private communication (2007).
- 6.
- R. H. BRUCK. A survey of binary systems. Springer-Verlag, Berlin, 1958. MR 0093552 (20:76)
- 7.
- R. P. BURN. Finite Bol loops I. Math. Proc. Cambridge Philos. Soc. 84(3) (1978), 53-66. MR 0492030 (58:11194)
- 8.
- The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.4.9; 2006. http://www.gap-system.org.
- 9.
- S. HEISS. Self-invariant 1-factorizations of complete graphs, submitted for publication.
- 10.
- B. HUPPERT. Endliche Gruppen I, Springer-Verlag, Berlin, Heidelberg, 1967. MR 0224703 (37:302)
- 11.
- H. KIECHLE. Theory of K-loops. Lecture Notes in Mathematics, 1778. Springer, Berlin, 2002. MR 1899153 (2003d:20109)
- 12.
- H. KIECHLE and G. P. NAGY. On the extension of involutorial Bol loops. Abh. Math. Semin. Univ. Hamb. 72, 235-250 (2002). MR 1941556 (2003m:20095)
- 13.
- E. KOLB and A. KREUZER. Geometry of kinematic
 -loops. Abh. Math. Sem. Univ. Hamburg 65 (1995), 189-197. MR 1359127 (96k:20150) - 14.
- B. MORTIMER. The modular permutation representations of the known doubly transitive groups. Proc. London Math. Soc. (3) 41 (1980), 1-20. MR 579714 (81f:20004)
- 15.
- G. P. NAGY. Solvability of universal Bol
 -loops. Comm. Algebra, 26(2) (1998), 549-555. MR 1604103 (98k:20112) - 16.
- G. P. NAGY. On the structure and number of small Frattini Bol 2-loops. Math. Proc. Camb. Philos. Soc. 141, No. 3, 409-419 (2006). MR 2281406 (2008a:20102)
- 17.
- G. P. NAGY. A class of simple proper Bol loops. Manuscripta Math. 127, No. 1, 81-88 (2008). MR 2429915
- 18.
- R. STEINBERG. Endomorphisms of linear algebraic groups. Memoirs of the American Mathematical Society, No. 80, American Mathematical Society, Providence, R.I. 1968. MR 0230728 (37:6288)
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Additional Information:
Gábor
P.
Nagy
Affiliation:
Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary
Address at time of publication:
Mathematisches Institut, Universität Würzburg, Am Hubland, D-97070 Würzburg, Germany
Email:
nagyg@math.u-szeged.hu
DOI:
10.1090/S0002-9947-09-04646-7
PII:
S 0002-9947(09)04646-7
Received by editor(s):
July 25, 2007
Received by editor(s) in revised form:
September 19, 2007
Posted:
May 28, 2009
Additional Notes:
This paper was written during the author's Marie Curie Fellowship MEIF-CT-2006-041105.
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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