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1d

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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 
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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 
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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 
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Realizing a monoid as $\mathrm{End}(G)$ for some graph $G$
Actually, their theorem states this under some cardinality constraints: gdz.sub.unigoettingen.de/… 
Nov 27 
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Realizing a monoid as $\mathrm{End}(G)$ for some graph $G$
Are loops allowed? 
Nov 27 
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Powers of finite simple groups
Oh, I see: mathoverflow.net/a/53162/24165 
Nov 23 
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Powers of finite simple groups
The automorphism groups of finite simple groups are well known. So, we have to calculate the (nonreduced) Euler function $\phi_n(G)$ (ie. the number of generating ntuples). 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 
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bounding from below the cardinality of a set of generators of the $n$fold cartesian product group of a finite group
See (my answer to) a similar question: mathoverflow.net/q/187736/24165 . 
Nov 22 
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Is the AmitsurLevitzki identity essentially unique?
... and why "combinatorics"? 
Nov 22 
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Is the AmitsurLevitzki identity essentially unique?
Why this is tagged "commutative algebra"? 
Nov 20 
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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 
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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 
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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 
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Explicitly showing that a free group is LERF
Surely, there is an algorithm for finding this finiteindex subgroup and the free complement in this subgroup. Just look at the proof of Hall's freefactor theorem. It is quite easy using Stallings graphs.. 
Nov 9 
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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 finiteindex 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 
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Fantastic properties of Z/2Z
I added these features, thanks, @Sam. 
Nov 9 
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Does the linear automorphism group determine the vector space?
Thanks, @Todd. I corrected the number. 
Nov 9 
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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 
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Fantastic properties of Z/2Z
@Denis, of course not. The infinite dihedral group $Z/2Z*Z/2Z$ has elements of infinite order. 
Nov 3 
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Fantastic properties of Z/2Z
@Todd, I understand you but I prefer to use slightly different terminology. See this discussion in comments: mathoverflow.net/q/92972/24165 