Related papers: Centralisers of formal maps

Let G be a compact real Lie group, and let f be an irreducible complex character of G, of degree > 1. We show that there exists an element g of G, of finite order, such that f(g)=0. We also give an unpublished result of Deligne, about…

In this paper we study the longstanding conjecture of whether there exists a noninner automorphism of order $p$ for a finite non-abelian $p$-group. We prove that if $G$ is a finite non-abelian $p$-group such that $G/Z(G)$ is powerful then…

Let G be a connected linear algebraic group defined over an algebraically closed field k and H be a finite abelian subgroup of G whose order is prime to char(k). We show that the essential dimension of G is bounded from below by rank(H) -…

Let $G$ be a finitely generated abelian-by-finite group and $k$ a field of characteristic $p\ge 0$. The Euler class $[k_G]$ of $G$ over $k$ is the class of the trivial $kG$-module in the Grothendieck group $G_0(kG)$. We show that $[k_G]$…

If two G-manifolds are G-cobordant then characteristic numbers corresponding to the fixed point sets (submanifolds) of subgroups of G and to normal bundles to these sets coincide. We construct two analogues of these characteristic numbers…

Let $G$ be a finite group and let $k$ be a sufficiently large finite field. Let $R(G)$ denote the character ring of $G$ (i.e. the Grothendieck ring of the category of ${\mathbb{C}}G$-modules). We study the structure and the representations…

We give a geometric characterisation of those groups that arise as fixed subgroups of finite-order untwisted automorphisms of right-angled Artin groups (RAAGs). They are precisely the fundamental groups of a class of compact special cube…

In our previous papers we introduced categorical invariants, which are, roughly speaking, sets of triangulated subcategories in a given triangulated category and their quotients. Here is extended the list of examples, where these sets are…

We prove several structural results on definably compact groups G in o-minimal expansions of real closed fields, such as (i) G is definably an almost direct product of a semisimple group and a commutative group, and (ii) the group (G, .) is…

Let $q$ be a prime, $n$ a positive integer and $A$ an elementary abelian group of order $q^r$ with $r\geq2$ acting on a finite $q'$-group $G$. The following results are proved. We show that if all elements in $\gamma_{r-1}(C_G(a))$ are…

Let $p$ be a prime and $\mathbb{F}_p$ be a finite field of $p$ elements. Let $\mathbb{F}_pG$ denote the group algebra of the finite $p$-group $G$ over the field $\mathbb{F}_p$ and $V(\mathbb{F}_pG)$ denote the group of normalized units in…

Let $p$ be a prime and let $G$ be a finite $p$-group. We show that the isomorphism type of the maximal abelian direct factor of $G$, as well as the isomorphism type of the group algebra over $\mathbb F_p$ of the non-abelian remaining direct…

We study the essential dimension of a finite group G over a field K. A generalization of the central extension theorem of Buhler and Reichstein (Compositio Math. 106 (1997) 159-179, Theorem 5.3) is obtained. We also get lower bounds of…

The structure of finite and locally finite groups in which every element has prime power order (CP-groups) is well known. In this paper we note that the combination of our earlier results with the available information on the structure of…

In this report we summarize this work, all finite simple groups $G$ can determined uniformly using their orders $|G|$ and the set $\pi_e(G)$ of their element orders.

This paper is primarily concerned with studying finite-dimensional anti-commutative nonassociative algebras in which every centralizer is an ideal. These are shown to be anti-associative and are classified over a general field $F$; in…

Every end of an infinite graph $ G $ defines a tangle of infinite order in $ G $. These tangles indicate a highly cohesive substructure in the graph if and only if they are closed in some natural topology. We characterize, for every finite…

Let X and Y be commuting nilpotent K-endomorphisms of a vector space V, where K is a field of characteristic p >= 0. If F=K(t) is the field of rational functions on the projective line, consider the K(t)-endomorphism A=X+tY of V. If p=0, or…

We study centralizers of elements in domains. We generalize a result of the author and Small, showing that if $A$ is a finitely generated noetherian domain and $a\in A$ is not algebraic over the extended centre of $A$, then the centralizer…

Let $k(G)$ be the number of conjugacy classes of finite groups $G$ and $\pi_e(G)$ be the set of the orders of elements in $G$. Then there exists a non-negative integer $k$ such that $k(G)=|\pi_e(G)|+k$. We call such groups to be $co(k)$…