1,687 reputation
418
bio website halgebra.math.msu.su/staff/…
location Moscow
age
visits member for 1 year, 10 months
seen Apr 1 at 17:06

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?
Aug
31
comment Basis removal gives a basis
@Will and domotorp: you are right of course; I edited this part. That was an incorrect generalisation of the 3-dimensional case.
Aug
31
revised Basis removal gives a basis
deleted 36 characters in body
Aug
30
comment Basis removal gives a basis
@fedja, if there is a pair of twins, then the other vectors must lie in some hyperplane $U$, because otherwise we would have a basis avoiding these twins and the harmony would give a basis containing the twins; this is a contradiction. So, all vectors except this pair of twins is a harmonic subset of $U$.
Aug
30
answered Embedding of a “quotient graph”
Aug
28
awarded  Nice Question
Aug
28
comment Basis removal gives a basis
@Gjergji: honestly, there are no research-level motivations. It was intended to be a problem for students (with the integer 10 probably) but --- I discovered that my question seems to be not so easy (for me). So, if there is a simple solution for 10, I shall be glad.
Aug
28
comment Basis removal gives a basis
@Gerry, it does not matter whether we are speaking about bases of $X$ (= bases of $\langle X\rangle$) or about bases of the whole space $V$. The answers will be obviously the same.
Aug
28
comment Basis removal gives a basis
@Gerry, A basis of a set of vectors is its maximal linearly independent subset. So, Joël and Tom are right. Thank you, Tom.
Aug
27
asked Basis removal gives a basis
Aug
25
revised Is there a better description of this class of discrete groups?
added 100 characters in body