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bio website halgebra.math.msu.su/staff/…
location Moscow
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visits member for 2 years, 6 months
seen 23 hours ago

Nov
9
comment Possible cardinality and weight of an ordered field
Taras, you may write an answer and accept your own answer to make the question "closed".
Nov
9
comment Explicitly showing that a free group is LERF
Surely, there is an algorithm for finding this finite-index subgroup and the free complement in this subgroup. Just look at the proof of Hall's free-factor theorem. It is quite easy using Stallings graphs..
Nov
9
comment Explicitly showing that a free group is LERF
Pablo, every f.g. subgroup $M$ of a f.g. free group $F$ is a free factor of a finite-index subgroup of $F$. So, the problem is reduced to the case where $M$ is a free factor of $F$, where it is quite easy.
Nov
9
comment Fantastic properties of Z/2Z
I added these features, thanks, @Sam.
Nov
9
revised Fantastic properties of Z/2Z
added 189 characters in body
Nov
9
comment Does the linear automorphism group determine the vector space?
Thanks, @Todd. I corrected the number.
Nov
9
revised Does the linear automorphism group determine the vector space?
edited body
Nov
9
comment Fantastic properties of Z/2Z
@Sam, I bet your single identity forms a basis of identities of the group. (This means that all other identities are consequences of this one.)
Nov
9
revised Does the linear automorphism group determine the vector space?
added 192 characters in body
Nov
8
revised Does the linear automorphism group determine the vector space?
added 23 characters in body
Nov
8
answered Does the linear automorphism group determine the vector space?
Nov
3
comment Fantastic properties of Z/2Z
@Denis, of course not. The infinite dihedral group $Z/2Z*Z/2Z$ has elements of infinite order.
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).