A note on computing involution centralizers
نویسندگان
چکیده
For a black box group G and t an involution of G we describe a computational procedure which produces elements of CG(t) by making use of the local fusion graph F(G, X), where X is the G-conjugacy class of t.
منابع مشابه
On centralizers of prime rings with involution
Let $R$ be a ring with involution $*$. An additive mapping $T:Rto R$ is called a left(respectively right) centralizer if $T(xy)=T(x)y$ (respectively $T(xy)=xT(y)$) for all $x,yin R$. The purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving left centralizers.
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For any group G, let C(G) denote the set of centralizers of G.We say that a group G has n centralizers (G is a Cn-group) if |C(G)| = n.In this note, we prove that every finite Cn-group with n ≤ 21 is soluble andthis estimate is sharp. Moreover, we prove that every finite Cn-group with|G| < 30n+1519 is non-nilpotent soluble. This result gives a partial answer to aconjecture raised by A. Ashrafi in ...
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Introduction In this talk all groups are finite (by definition), and all simple groups are non-abelian. Let us first define our terms: an involution in a group G is an element t of order 2, i.e. t = 1 and t 6= 1. Its centralizer CG(t) is the subgroup of elements which commute with it, so CG(t) = {g ∈ G | tg = gt}. It has long been accepted in abstract group theory that the way to study simple g...
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ورودعنوان ژورنال:
- J. Symb. Comput.
دوره 54 شماره
صفحات -
تاریخ انتشار 2013