‎motivated by a celebrated theorem of schur‎, ‎we show that if~$gamma$ is a normal subgroup of the full automorphism group $aut(g)$ of a group $g$ such that $inn(g)$ is contained in $gamma$ and $aut(g)/gamma$ has no uncountable abelian subgroups of prime exponent‎, ‎then $[g,gamma]$ is finite‎, ‎provided that the subgroup consisting of all elements of $g$ fixed by $gamma$ has finite index‎. ‎so...

We prove that given any n-pointed prestable curve C of genus g with linearly reductive automorphism group Aut(C), there exists an Aut(C)equivariant miniversal deformation of C over an affine variety W . In other words, we prove that the algebraic stack Mg,n parametrizing n-pointed prestable curves of genus g has an étale neighborhood of [C] isomorphic to the quotient stack [W/Aut(C)].

We prove that the automorphism group of any non-abelian free group F is complete. The key technical step in the proof: the set of all conjugations by powers of primitive elements is first-order parameter-free definable in the group Aut(F ). Introduction In 1975 J. Dyer and E. Formanek [2] had proved that the automorphism group of a finitely generated non-abelian free group F is complete (that i...

Let $G$ be a group and $Aut(G)$ be the group of automorphisms of‎ ‎$G$‎. ‎For any natural‎ number $m$‎, ‎the $m^{th}$-autocommutator subgroup of $G$ is defined‎ ‎as‎: ‎$$K_{m} (G)=langle[g,alpha_{1},ldots,alpha_{m}] |gin G‎,‎alpha_{1},ldots,alpha_{m}in Aut(G)rangle.$$‎ ‎In this paper‎, ‎we obtain the $m^{th}$-autocommutator subgroup of‎ ‎all finite abelian groups‎.

Question. Given a connected curve C 0 , proper and smooth over a field K of characteristic p, given a subgroup H ⊂ Aut(C 0); can we lift the pair (C 0 , H) to characteristic zero? ((We shall see that the answer is " NO " in general; for cyclic groups we conjecture that the answer is " YES " .)) Example (1) (Roquette). Consider the normalization of the completion of the curve given by the affine...

BugReports https://bugs.r-project.org NeedsCompilation yes Author José Pinheiro [aut] (S version), Douglas Bates [aut] (up to 2007), Saikat DebRoy [ctb] (up to 2002), Deepayan Sarkar [ctb] (up to 2005), EISPACK authors [ctb] (src/rs.f), Siem Heisterkamp [ctb] (Author fixed sigma), Bert Van Willigen [ctb] (Programmer fixed sigma), R-core [aut, cre] Maintainer R-core Reposi...

Let X be a right-angled hyperbolic building. We show that the lattices in Aut(X) share many properties with tree lattices. For example, we characterise the set of covolumes of uniform and of nonuniform lattices in Aut(X), and show that the group Aut(X) admits an infinite ascending tower of uniform and of nonuniform lattices. These results are proved by constructing a functor from graphs of grou...

It is shown that Aut(L ~ is naturally isomorphic to Aut(L) x Aut(Q) when L is a directly and exponentially indecomposable lattice, Q a non-empty connected poset, and one of the following holds: Q is arbitrary but L is a jm-lattice, Q is finitely factorable and L is complete with a join-dense subset of completely join-irreducible elements, or L is arbitrary but Q is finite. A problem of J6nsson ...