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Nov
9 |
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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 |
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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. |