COMMUTATIVITY DEGREES OF WREATH PRODUCTS OF FINITE ABELIAN GROUPS
نویسندگان
چکیده
منابع مشابه
Commutativity Degrees of Wreath Products of Finite Abelian Groups
We compute commutativity degrees of wreath products A o B of finite abelian groups A and B . When B is fixed of order n the asymptotic commutativity degree of such wreath products is 1/n2. This answers a generalized version of a question posed by P. Lescot. As byproducts of our formula we compute the number of conjugacy classes in such wreath products, and obtain an interesting elementary numbe...
متن کاملFinite groups with three relative commutativity degrees
For a finite group $G$ and a subgroup $H$ of $G$, the relative commutativity degree of $H$ in $G$, denoted by $d(H,G)$, is the probability that an element of $H$ commutes with an element of $G$. Let $mathcal{D}(G)={d(H,G):Hleq G}$ be the set of all relative commutativity degrees of subgroups of $G$. It is shown that a finite group $G$ admits three relative commutativity degrees if a...
متن کاملfinite groups with three relative commutativity degrees
for a finite group $g$ and a subgroup $h$ of $g$, the relative commutativity degree of $h$ in $g$, denoted by $d(h,g)$, is the probability that an element of $h$ commutes with an element of $g$. let $mathcal{d}(g)={d(h,g):hleq g}$ be the set of all relative commutativity degrees of subgroups of $g$. it is shown that a finite group $g$ admits three relative commutativity degrees if a...
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Let G be a group which has a finite number hn(G) of irreducible linear representations in GLn(C) for all n ≥ 1. Let ζ(G, s) = P∞ n=1 hn(G)n −s be its representation zeta function. First, in case G = H oXQ is a permutational wreath product with respect to a permutation group Q on a finite set X, we establish a formula for ζ(G, s) in terms of the zeta functions of H and of subgroups of Q, and of ...
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Let P2(G) be defined as the probability that any two elements selected at random from the group G, commute with one another. If G is an Abelian group, P2(G) = 1, so our interest lies in the properties of the commutativity of nonAbelian groups. Particular results include that the maximum commutativity of a non-Abelian group is 5/8, and this degree of commutativity only occurs when the order of t...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2008
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972708000038