On loops which have dihedral 2-groups as inner mapping groups
نویسندگان
چکیده
منابع مشابه
On finite loops whose inner mapping groups have small orders
We investigate the situation that the inner mapping group of a loop is of order which is a product of two small prime numbers and we show that then the loop is soluble.
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The Cayley–Dickson loop Qn is the multiplicative closure of basic elements of the algebra constructed by n applications of the Cayley–Dickson doubling process (the first few examples of such algebras are real numbers, complex numbers, quaternions, octonions, sedenions). We establish that the inner mapping group Inn(Qn) is an elementary abelian 2-group of order 2 −2 and describe the multiplicati...
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In this paper we consider finite loops of specific order and we show that certain abelian groups are not isomorphic to inner mapping groups of these loops. By using our results we are able to construct a finite solvable group of order 120 which is not isomorphic to the multiplication group of a finite loop.
متن کاملA class of commutative loops with metacyclic inner mapping groups
We investigate loops defined upon the product Zm × Zk by the formula (a, i)(b, j) = ((a + b)/(1 + tf (0)f (0)), i + j), where f(x) = (sx + 1)/(tx + 1), for appropriate parameters s, t ∈ Z∗m. Each such loop is coupled to a 2-cocycle (in the group-theoretical sense) and this connection makes it possible to prove that the loop possesses a metacyclic inner mapping group. If s = 1, then the loop is ...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1995
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700014520