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5h
comment Do all exact 1 -> A -> AxB -> B -> 1 split for finite groups?
Could you write down the references? One of the links is not working; after inquiry it's: Goldstein, Daniel, Guralnick, Robert The direct product theorem for profinite groups. J. Group Theory 9 (2006), no. 3, 317-322.
5h
comment if 0→A→A⊕B→B→0 is an exact sequence of finitely generated modules over a commutative Noetherian ring, then the exact sequence does split
On the analogous question for finite groups: mathoverflow.net/questions/80002
5h
comment Handbook Homogeneous Space Examples?
I'm not sure what you mean by $G/H\simeq G'/H'$, but is $G$ is not isomorphic to $G'$ it's hard to call this "equivalent description".
6h
comment to what extent is a reductive group hyperbolic?
Most likely, none. These property imply that cocompact lattices have a lot of quotients (and in particular admit infinite normal subgroups of infinite index), while most higher rank groups $G(F)$ admit just-infinite cocompact lattices.
13h
comment Isotopy class of closed 2-ball embedded in R^3
It's not clear to me that an embedding mapping the sphere to a horned sphere can't be isotopic (= homotopic where each step is an embedding) to a standard embedding. Isn't the horned sphere defined as a uniform limit of smooth embeddings?
1d
comment A non locally compact group of finite topological dimension?
@YonatanHarpaz for spaces, in dimension 1 there are examples as well. Just take the 1-skeleton of a graph not of finite degree, endowed with either the direct limit topology (of its finite subgraphs), or with its distance topology.
1d
comment Symplectic group over integers and finite fields
Reduction modulo $p$ of a group makes no sense, indeed. Thanks to Piotr who guess what you had in mind and didn't write...
1d
comment Symplectic group over integers and finite fields
I'm not sure what you mean by your tensor product notation between a group and a field.
1d
revised A non locally compact group of finite topological dimension?
edited title
1d
comment HNN extension group with finitely generated base
You can cook up an example with $H=BS(1,2)^2$ and a well-chosen choice of $B$. Also there are examples where $H$ is Thompson's group $F$.
1d
comment Solvable Lie algebra whose nilradical is not characteristic
Thanks for your answer. Google "characteristic ideal" first points to groupprops.subwiki.org/wiki/Characteristic_ideal_of_a_Lie_ring which defines it as an ideal stable under automorphisms, which is indeed a distinct definition.
1d
comment HNN extension group with finitely generated base
I doubt you can get a general answer other than just a restatement. The answer is quite subtle even in the case when $H$ is metabelian (of course, a sufficient condition is that $B$ is finitely presented, but it's not necessary).
1d
revised Can approximately periodic functions be perturbed to periodic functions on a locally compact group?
edited tags
1d
comment Can approximately periodic functions be perturbed to periodic functions on a locally compact group?
An argument involving only general topology and group theory? You don't want measure theory and integration, convolutions, etc? these are usually useful tools in this context...
1d
comment Can we always attain another prime via inserting digits between the digits of a fixed prime?
I just suggest to not use such codes in title. The title is supposed to convey some idea of the subject, which helps me to decide if I want to open the post without further inquiry. Possibly you know by heart all OEIS numbers. I don't. Also many readers don't even know that what "OEIS" stands for. The new title looks fine to me.
1d
comment Can we always attain another prime via inserting digits between the digits of a fixed prime?
Could we avoid using these OEIS numbers in the title? The title is addressed to human beings, not robots.
1d
comment Sets of matrices which are irreducible but not strongly irreducible
We can't really expect these two mechanisms to exhaust, since the two mechanisms can be melted using a tensor product. "Is there a precise characterization" is a bit vague, since the definition is a precise characterization. Reasonably, we can ask, given an irreducible representation of a semigroup, whether we can have a reasonable description of those invariant finite union of subspaces (by the way, there is a natural sub-topology of the Zariski topology, called linear topology, that is relevant here, for which the closed subsets are the finite unions of linear subspaces).
2d
comment A question about generating set of groups and epimorphism
... I don't know what you checked, but these groups are definitely finitely generated and the proof is quite standard.
2d
revised Primary structures in $\mathbb Q$
edited tags
2d
comment p-groups with unique normal minimal subgroup
OK actually I read correctly the question mut misread the other question I linked. Certainly the class is big; it contains for instance the upper unipotent groups over fields of prime order. I would not expect any kind of reasonable classification.