bio  website  sci.ccny.cuny.edu/~benjamin 

location  New York City  
age  41  
visits  member for  2 years, 10 months 
seen  2 hours ago  
stats  profile views  6,586 
I am an algebraist interested in a broad range of areas. I've worked on semigroups, geometric group theory, algebraic combinatorics, representation theory, selfsimilar groups (aka automaton groups), profinite groups and random walks on semigroups and groups. I've been particularly interested in interactions between these areas and Computer Science and am fond of algorithmic questions. I've also dabbled with operator algebras associated to etale groupoids and inverse semigroups. Currently, I am interested in applications of finite semigroup theory to finite state Markov chains.
My blog is http://bensteinberg.wordpress.com/author/bsteinbg/
2h

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Is any finitely generated nilpotent pro$p$ group necessarily the pro$p$ completion of some finitely generated nilpotent group?
Khalid, are there only countably many isomorphism types of fg nilpotent prop groups? There are only countably many isomorphism classes of prop completions of fg nilpotent groups since fg nilpotent groups are fp. 
11h

reviewed  Approve suggested edit on primeconstellations tag wiki excerpt 
1d

reviewed  Close Recreating the wheel 
1d

reviewed  Reject suggested edit on nontrivial theorems with trivial proofs 
1d

comment 
Results about the existence of solutions in groups
Look up Makanin for free groups and Rips/Sela for hyperbolic groups where systems if equations are considered. 
1d

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Are semigroups with finitetoone right multiplication “moving”?
I suppose right cancellative can be replaced by a uniform bound on the degree of finitetooneness. 
Apr 21 
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Polytopes generated as the convex hull of the orbit of a finite reflection group acting on a given vector
Look for Wpermutohedra or Coxeter group and permutohedra. 
Apr 17 
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Computational complexity of deciding isomorphism of rational polyhedral cones
This is the tricky part to do in a way with reasonable complexity. 
Apr 15 
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Schreier's index formula
Free prosolvable groups and free prop groups satisfy Schreier's formula. 
Apr 15 
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Schreier's index formula
@HJRW, this is why I hedged to the rf case. 
Apr 14 
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Schreier's index formula
The intersection of all the terms of the derived series is trivial because the free group is residually a finite pgroup and hence residually solvable. So you do get a free group and there is no contradiction. 
Apr 14 
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Computational complexity of deciding isomorphism of rational polyhedral cones
I am not so convinced here. The Hermite form seems to have to do with generating the same lattice. I am asking for isomorphic cones. I don't see that this is the same as checking the Hermite form for a matrix. Can you give details? 
Apr 14 
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Computational complexity of deciding isomorphism of rational polyhedral cones
The cone might not be pointed, so there may not be a hilbert basis. 
Apr 14 
answered  Schreier's index formula 
Apr 14 
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Schreier's index formula
Let me hedge and assume the group is residually finite. 
Apr 14 
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Schreier's index formula
I believe only a free group satisfies Schreier's index formula and that this was first observed by van den Dries and Lubotzsky, who proved a prop analogue. 
Apr 14 
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Computational complexity of deciding isomorphism of rational polyhedral cones
I will take a look. You are saying to cones are equivalent iff the corresponding matrices have the same Hermite normal form? 
Apr 9 
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Generalized permutahedron and random polytopes
I think people generally use permutohedron to refer to the convex hull of all permutations of the entries of any vector with distinct entries. If the entries are distinct you always get the same face lattice, which is just the dual to the face lattice of the braid hyperplane arrangement. Maybe look at wwwmath.mit.edu/~apost/papers/permutohedron.pdf 
Apr 8 
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automorphism of finitly generated group
Inna Bumagin and Daniel Wise proved it. sciencedirect.com/science/article/pii/S0022404904003111 
Apr 8 
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automorphism of finitly generated group
It need not be finitely generated. Any countable group is the outer automorphism group of a fg group. 