bio | website | halgebra.math.msu.su/staff/… |
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location | Moscow | |
age | ||
visits | member for | 3 years, 2 months |
seen | Jul 28 at 2:43 | |
stats | profile views | 1,680 |
Nov 9 |
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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 |
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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 |
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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 |
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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 |
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Fantastic properties of Z/2Z
@Denis, of course not. The infinite dihedral group $Z/2Z*Z/2Z$ has elements of infinite order. |
Nov 3 |
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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 |
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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 |
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Which groups are LERF?
It is not LERF because of the Mikhailova subgroup with undecidable membership problem. |
Oct 31 |
awarded | Necromancer |
Oct 9 |
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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 |
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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 |
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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 |
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Are infinite groups “locally topologizable”?
I have a Russian edition. This is Chapter 10, Section 31, Subsection 3. |
Aug 25 |
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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 $Nv$. |