Finite loops with dihedral inner mapping groups are solvable
نویسندگان
چکیده
منابع مشابه
finite bci-groups are solvable
let $s$ be a subset of a finite group $g$. the bi-cayley graph ${rm bcay}(g,s)$ of $g$ with respect to $s$ is an undirected graph with vertex set $gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid xin g, sin s}$. a bi-cayley graph ${rm bcay}(g,s)$ is called a bci-graph if for any bi-cayley graph ${rm bcay}(g,t)$, whenever ${rm bcay}(g,s)cong {rm bcay}(g,t)$ we have $t=gs^alpha$ for some $...
متن کاملBruck Loops with Abelian Inner Mapping Groups
Bruck loops with abelian inner mapping groups are centrally nilpotent of class at most 2.
متن کاملOn 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.
متن کاملOn abelian inner mapping groups of finite loops
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 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2004
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2002.09.001