All finite automorphic loops have the elementwise Lagrange property
نویسندگان
چکیده
منابع مشابه
Loops and the Lagrange Property
Let F be a family of finite loops closed under subloops and factor loops. Then every loop in F has the strong Lagrange property if and only if every simple loop in F has the weak Lagrange property. We exhibit several such families, and indicate how the Lagrange property enters into the problem of existence of finite simple loops. The two most important open problems in loop theory, namely the e...
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These notes accompany a series of three lectures on automorphic loops to be delivered by the author at Workshops Loops ’15 (Ohrid, Macedonia, 2015). Automorphic loops are loops in which all inner mappings are automorphisms. The first paper on automorphic loops appeared in 1956 and there has been a surge of interest in the topic since 2010. The purpose of these notes is to introduce the methods ...
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An automorphic loop (or A-loop) is a loop whose inner mappings are automorphisms. Every element of a commutative A-loop generates a group, and (xy)−1 = x−1y−1 holds. Let Q be a finite commutative A-loop and p a prime. The loop Q has order a power of p if and only if every element of Q has order a power of p. The loop Q decomposes as a direct product of a loop of odd order and a loop of order a ...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2015
ISSN: 0035-7596
DOI: 10.1216/rmj-2015-45-4-1101