On the Uniqueness of Loops M(g, 2)
نویسنده
چکیده
Let G be a finite group and C2 the cyclic group of order 2. Consider the 8 multiplicative operations (x, y) 7→ (xiyj)k, where i, j, k ∈ {−1, 1}. Define a new multiplication on G × C2 by assigning one of the above 8 multiplications to each quarter (G × {i}) × (G × {j}), for i, j ∈ C2. When G is nonabelian then exactly four assignments yield Moufang loops that are not associative; all (anti)isomorphic, known as loops M(G, 2).
منابع مشابه
A Class of Bol Loops with a Subgroup of Index Two
Let G be a finite group and C2 the cyclic group of order 2. Consider the 8 multiplicative operations (x, y) 7→ (xiyj)k, where i, j, k ∈ {−1, 1}. Define a new multiplication on G × C2 by assigning one of the above 8 multiplications to each quarter (G× {i})× (G× {j}), for i, j ∈ C2. We describe all situations in which the resulting quasigroup is a Bol loop. This paper also corrects an error in P....
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تاریخ انتشار 2004