for $q in {7,8,9,11,13,16}$, we consider the primitive actions of $l_2(q)$ and use key-moori method 1 as described in [codes, designs and graphs from the janko groups {$j_1$} and{$j_2$}, {em j. combin. math. combin. comput.}, {bf 40} (2002) 143--159., correction to: ``codes, designs and graphs from the janko groups{$j_1$} and {$j_2$}'' [j. combin. math. combin. comput. {bf 40} (2002) 143--159],...

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...

We study centralisers of finite order automorphisms of the generalised Thompson groups Fn,∞ and conjugacy classes of finite subgroups in finite extensions of Fn,∞. In particular we show that centralisers of finite automorphisms in Fn,∞ are either of type FP∞ or not finitely generated. As an application we deduce the following result about the Bredon type of such finite extensions: any finite ex...

Two distinct projections of finite rank m are adjacent if their difference is an operator two or, equivalently, the intersection images (m−1)-dimensional. We extend this adjacency relation on other conjugacy classes finite-rank self-adjoint operators which leads to a natural generalization Grassmann graphs. Let C be class formed by with eigenspaces dimension greater than 1. Under assumption tha...

We consider the graph whose vertex set is a conjugacy class C consisting of finite-rank self-adjoint operators on complex Hilbert space H. The dimension H assumed to be not less than 3. In case when from have two eigenvalues only, we obtain Grassmann formed by k-dimensional subspaces H, where k smallest eigenspaces. Chow's theorem describes automorphisms this for k>1. Under assumption that more...

Abstract It is proved that every finitely generated profinite group with fewer than $$2^{\aleph _0}$$ 2 ℵ 0 conjugacy classes of elements infinite order finite.