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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
Aug
25
comment Is there a better description of this class of discrete groups?
Almost. I replaced "set" with "class" in the deTeXified sentence.
Aug
25
revised Is there a better description of this class of discrete groups?
added 38 characters in body
Aug
25
answered Is there a better description of this class of discrete groups?
Aug
23
comment On “super connected” graphs
"we can take any of these, say $H_1$, and $H_1 \cup \{a, b\}$ will be connected..." As far as I understand, we should take a component $H_1$ such that $H_1 \cup \{a, b\}$ is connected. It is not automatically.
Aug
8
comment Abelian subgroups of maximum order in $p$-Groups
I do not understand $\frac{p+3}{2}$. The index should be a power of $p$, right?
Aug
8
comment Abelian subgroups of maximum order in $p$-Groups
@Dietrich, no, it is not.