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visits member for 2 years, 6 months
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Nov
3
comment Fantastic properties of Z/2Z
@Todd, I understand you but I prefer to use slightly different terminology. See this discussion in comments: mathoverflow.net/q/92972/24165
Nov
3
comment Fantastic properties of Z/2Z
@Emil, every group of exponent two is a direct product of several two-element groups (if you believe the Axiom of Choice).
Nov
3
awarded  Nice Answer
Nov
3
comment Which groups are LERF?
It is not LERF because of the Mikhailova subgroup with undecidable membership problem.
Oct
31
awarded  Necromancer
Oct
9
comment Two questions about axiomatic rank of groups
@M.Shahryari, no way. Consider the variety of abelian groups. It satisfies the metabelian law $[[x,y],[z,t]]=1$ or the nilpotency law $[[x,y],z]=1$. Do you believe that these laws are equivalent to two-variable laws?
Oct
8
comment Two questions about axiomatic rank of groups
To question 1 the answer is obviously negative. Just consider the trivial variety, it has finite axiomatic rank but satisfies all identities.
Aug
27
comment Are infinite groups “locally topologizable”?
It is on page 339 of English edition. Unfortunately, Google preview rejects to show this page to me (but I may read the table of contents).
Aug
26
comment Are infinite groups “locally topologizable”?
I have a Russian edition. This is Chapter 10, Section 31, Subsection 3.
Aug
25
comment Invariant planes of a nilpotent matrix with two Jordan blocks of size two
This is the description of all of them, because any invariant subspace containing a vector $v$ shoud contain $Nv$.
Aug
25
comment Invariant planes of a nilpotent matrix with two Jordan blocks of size two
Take any vector $v$ not belonging to the kernel of $N$ and consider the space $\langle v,Nv\rangle$. This family and the kernel of $N$ are all spaces you ask about.
Aug
24
awarded  Self-Learner
Aug
23
answered A sequence of subsets of an infinite group
Aug
23
answered Are infinite groups “locally topologizable”?
Aug
23
comment A sequence of subsets of an infinite group
A related question: mathoverflow.net/q/179177/24165 .
Aug
23
asked Are infinite groups “locally topologizable”?
Jul
2
awarded  Curious
Jun
2
awarded  Yearling
Apr
24
comment An element $g$ in a group such that neither $g=1$ nor $g\ne 1$ can be proved.
@Dan, surely. What you said is basically Metatheorem 3.5.2 from my answer.
Mar
8
awarded  Popular Question