Impact
~20k
people reached
- 0 posts edited
- 1 helpful flag
- 343 votes cast
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. |