Anton Klyachko
Reputation
2,244
Top tag
Next privilege 2,500 Rep.
Create tag synonyms
 Jul 6 comment Group with finite outer automorphism group and large center I added some details. Jul 2 comment Group with finite outer automorphism group and large center Yves, "transposition" should read contrgradient ($X\mapsto (X^t)^{-1}$). Also, $\mbox{Aut}(Z(G))$ should read $\mbox{Aut}(G/Z(G))$. Dec 6 comment Is the free abstract group residually of rank d > 2? This rank was introduced by Malcev and is called special rank. Namely, The special rank of a group $G$ is the minimal $d$ such that every finitely generated subgroup of $G$ can be generated by $d$ elements. Dec 4 comment Is the free abstract group residually of rank d > 2? And why there are no such words $w(x,y)\in F_2$? Nov 27 comment Realizing a monoid as $\mathrm{End}(G)$ for some graph $G$ Actually, their theorem states this under some cardinality constraints: gdz.sub.uni-goettingen.de/… Nov 27 comment Realizing a monoid as $\mathrm{End}(G)$ for some graph $G$ Are loops allowed? Nov 27 comment Powers of finite simple groups Oh, I see: mathoverflow.net/a/53162/24165 Nov 23 comment Powers of finite simple groups The automorphism groups of finite simple groups are well known. So, we have to calculate the (non-reduced) Euler function $\phi_n(G)$ (ie. the number of generating n-tuples). In Section 1.1, Collins describes a technique of such calculations that allowed Hall (in 1936) to calculate, e.g., $\phi_2(A_5)=19\cdot 120$ (ie. $h_2(A_5)=19$). Nov 22 comment Bounding from below the cardinality of a set of generators of the $n$-fold cartesian product of a finite group See (my answer to) a similar question: mathoverflow.net/q/187736/24165 . Nov 22 comment Is the Amitsur-Levitzki identity essentially unique? ... and why "combinatorics"? Nov 22 comment Is the Amitsur-Levitzki identity essentially unique? Why this is tagged "commutative algebra"? Nov 20 comment Normal Covering of a Finite Group This Corollary 5.5 follows immediately from the theorem of Brodie, Chamberlain and Kapp, PAMS 1988, see Nick Gill's answer: mathoverflow.net/a/185604/24165 . Nov 9 comment Is the equational theory of commutative vN regular rings decidable? Thomas, every finitely generated associative commutative ring is residually finite. (For free rings (= polynomial rings), this is almost obvious.) Nov 9 comment Possible cardinality and weight of an ordered field Taras, you may write an answer and accept your own answer to make the question "closed". Nov 9 comment Explicitly showing that a free group is LERF Surely, there is an algorithm for finding this finite-index subgroup and the free complement in this subgroup. Just look at the proof of Hall's free-factor theorem. It is quite easy using Stallings graphs.. Nov 9 comment Explicitly showing that a free group is LERF Pablo, every f.g. subgroup $M$ of a f.g. free group $F$ is a free factor of a finite-index subgroup of $F$. So, the problem is reduced to the case where $M$ is a free factor of $F$, where it is quite easy. Nov 9 comment Fantastic properties of Z/2Z I added these features, thanks, @Sam. Nov 9 comment Does the linear automorphism group determine the vector space? Thanks, @Todd. I corrected the number. Nov 9 comment Fantastic properties of Z/2Z @Sam, I bet your single identity forms a basis of identities of the group. (This means that all other identities are consequences of this one.) Nov 3 comment Fantastic properties of Z/2Z @Denis, of course not. The infinite dihedral group $Z/2Z*Z/2Z$ has elements of infinite order.