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UNIQUELY 2-DIVISIBLE BOL LOOPS
- Source :
- Journal of Algebra and Its Applications. :591-601
- Publication Year :
- 2010
- Publisher :
- World Scientific Pub Co Pte Ltd, 2010.
-
Abstract
- Although any finite Bol loop of odd prime exponent is solvable, we show there exist such Bol loops with trivial center. We also construct finitely generated, infinite, simple Bruck loops of odd prime exponent for sufficiently large primes. This shows that the Burnside problem for Bruck loops has a negative answer.<br />Comment: 9 pages; v.2: new results, reformatted for journal submission; v.3; labels on nuclei switched around. V4: same paper, but the referee wanted a different title
- Subjects :
- Algebra and Number Theory
Mathematics::General Mathematics
Mathematics::Number Theory
Applied Mathematics
20N05
Group Theory (math.GR)
Center (group theory)
Prime (order theory)
Combinatorics
Negative - answer
Mathematics::Group Theory
Bol loop
Simple (abstract algebra)
FOS: Mathematics
Exponent
Finitely-generated abelian group
Moufang loop
Mathematics - Group Theory
Mathematics
Subjects
Details
- ISSN :
- 17936829 and 02194988
- Database :
- OpenAIRE
- Journal :
- Journal of Algebra and Its Applications
- Accession number :
- edsair.doi.dedup.....39ecb7bc7a04fac9492a1fc0188fb123
- Full Text :
- https://doi.org/10.1142/s0219498810004129