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Dec
14 |
comment |
Large abelian characteristic subgroups in abelian-by-countable groups
Thank you, Yves!! Surely, you mean $g(e_q)\in e_q+Vect(\dots)$ in the first paragraph. Also, $G_K$ in the second paragraph is the same as $G_K^Q$. Furthermore, I guess that the "easy play with commutators" is something like the following. The commutator of any matrix and an elementary matrix is finitely supported, i.e. this commutator lies in a finite-dimensional unitriangular subgroup $UT_n(K)$ which is nilpotent and, hence, any its non-trivial normal subgroup non-trivially intersects the centre, which consists of elementary matrices. |
Dec
14 |
asked | Large abelian characteristic subgroups in abelian-by-countable groups |
Dec
12 |
comment |
Commutator Width of a direct limit of hyperbolic groups
I do not understand. Any group having only finitely many conjugacy classes must have finite commutator width, because conjugate elements have the same commutator length. |
Dec
11 |
comment |
Applications of the Chinese remainder theorem
Excuse me, KConrad (and @Zack), I do not understand the problem about squares. Suppose that we have integers $a$ and $b$ such that $f(a)\ne0$ modulo $p^2$ and $f(b)\ne0$ modulo $q^2$, then CRT provides us with an integer $c$ equal to $a$ modulo $p^2$ and equal to $b$ modulo $q^2$. Thus, $f(c)=f(a)\ne0$ modulo $p^2$ and $f(c)=f(b)\ne0$ modulo $q^2$, which is a contradiction. Or I miss something? |
Nov
5 |
comment |
Minimal number of generators of subgroups of Noetherian groups
@Ian, indeed, "Are all finitely presented Noetherian groups virtually polycyclic? is (an open) Question 11.38 (due to S.V.Ivanov, 1990) from the Kourovka Notebook. |
Nov
4 |
awarded | Enlightened |
Nov
4 |
awarded | Nice Answer |
Nov
3 |
comment |
The rank of the intersection of subgroups of a free group
Igor, it was asked about the case, where one of the subgroups is of finite index. This is indeed an exercise on Schreier formula. |
Nov
3 |
revised |
Minimal number of generators of subgroups of Noetherian groups
added 7 characters in body |
Nov
3 |
answered | Minimal number of generators of subgroups of Noetherian groups |
Nov
3 |
comment |
Is there an infinite group with exactly two conjugacy classes?
@Gerry, I do not think this is a homework. An example can be easily constructed using iterated HNN-extensions. A finitely generated example also exists but this is a highly non-trivial result of D. Osin. |
Nov
2 |
accepted | Are compact simple groups homotopically non-abelian? |
Oct
31 |
comment |
Are compact simple groups homotopically non-abelian?
Here is the link: ams.org/journals/bull/1960-66-04/S0002-9904-1960-10487-9/… |
Oct
31 |
comment |
Are compact simple groups homotopically non-abelian?
Thank you, Ramiro, this is what I sought! |
Oct
31 |
asked | Are compact simple groups homotopically non-abelian? |
Oct
8 |
comment |
About sets with two mutually associative group structures
In particular, this means that the two groups must be isomorphic. |
Oct
1 |
awarded | Caucus |
Aug
31 |
comment |
A generalization of an old group problem
@nadal, (2) is not true (without additional assumptions); see Yves's comment. |
Aug
31 |
comment |
Basis removal gives a basis
Oh, thank you, @domotorp! |
Aug
31 |
comment |
Basis removal gives a basis
I do not understand about 28. Can you clarify? |