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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 group 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.
Nov
3
comment 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
Nov
3
comment Fantastic properties of Z/2Z
@Emil, every group of exponent two is a direct product of several two-element groups (if you believe the Axiom of Choice).