N 05 Commutants of Bol Loops of Odd Order
نویسندگان
چکیده
In this note we show that the commutant of a Bol loop of odd order is a subloop.
منابع مشابه
BOL LOOPS AND BRUCK LOOPS OF ORDER pq
Right Bol loops are loops satisfying the identity ((zx)y)x = z((xy)x), and right Bruck loops are right Bol loops satisfying the identity (xy)−1 = x−1y−1. Let p and q be odd primes such that p > q. Advancing the research program of Niederreiter and Robinson from 1981, we classify right Bol loops of order pq. When q does not divide p−1, the only right Bol loop of order pq is the cyclic group of o...
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A left Bol loop is a loop satisfying x(y(xz)) = (x(yx))z. The commutant of a loop is the set of all elements which commute with all elements of the loop. In a finite Bol loop of odd order or of order 2k, k odd, the commutant is a subloop. We investigate conditions under which the commutant of a Bol loop is not a subloop. In a finite Bol loop of order relatively prime to 3, the commutant generat...
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We study the commuting graph on elements of odd prime order in finite simple groups. The results are used in a forthcoming paper describing the structure of Bruck loops and Bol loops of exponent 2.
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Some associativity properties of a loop can be interpreted as certain closure configuration of the corresponding 3-net. It was known that the smallest non-associative loops with the so called left Bol property have order 8. In this paper, we determine the direction preserving collineation groups of the 3-nets belonging to these smallest Bol loops. For that, we prove some new results concerning ...
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تاریخ انتشار 2002