منابع مشابه
On finite $X$-decomposable groups for $X={1, 2, 3, 4}$
Let $mathcal {N}_G$ denote the set of all proper normal subgroups of a group $G$ and $A$ be an element of $mathcal {N}_G$. We use the notation $ncc(A)$ to denote the number of distinct $G$-conjugacy classes contained in $A$ and also $mathcal {K}_G$ for the set ${ncc(A) | Ain mathcal {N}_G}$. Let $X$ be a non-empty set of positive integers. A group $G$ is said to be $X$-d...
متن کاملon finite $x$-decomposable groups for $x={1, 2, 3, 4}$
let $mathcal {n}_g$ denote the set of all proper normal subgroups of a group $g$ and $a$ be an element of $mathcal {n}_g$. we use the notation $ncc(a)$ to denote the number of distinct $g$-conjugacy classes contained in $a$ and also $mathcal {k}_g$ for the set ${ncc(a) | ain mathcal {n}_g}$. let $x$ be a non-empty set of positive integers. a group $g$ is said to be $x$-d...
متن کاملComputable Completely Decomposable Groups
A completely decomposable group is an abelian group of the form ⊕ i Hi, where Hi ≤ (Q,+). We show that every computable completely decomposable group is ∆5-categorical. We construct a computable completely decomposable group which is not ∆4-categorical, and give an example of a computable completely decomposable group G which is ∆4-categorical but not ∆3-categorical. We also prove that the inde...
متن کاملOn the Mark and Markaracter Tables of Finite Groups
Let G be a finite group and C(G) be the family of representative conjugacy classes of subgroups of G. The matrix whose H,K-entry is the number of fixed points of the set G/K under the action of H is called the table of marks of G where H,K run through all elements in C(G). Shinsaku Fujita for the first time introduced the term “markaracter” to discuss marks for permutation representati...
متن کاملON THE CHARACTERISTIC DEGREE OF FINITE GROUPS
In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics and Computing
سال: 2008
ISSN: 1598-5865,1865-2085
DOI: 10.1007/s12190-007-0001-8