12,908 reputation
22880
bio website sci.ccny.cuny.edu/~benjamin
location New York City
age 41
visits member for 2 years, 10 months
seen 2 hours ago

I am an algebraist interested in a broad range of areas. I've worked on semigroups, geometric group theory, algebraic combinatorics, representation theory, self-similar 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
comment 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 pro-p groups? There are only countably many isomorphism classes of pro-p completions of fg nilpotent groups since fg nilpotent groups are fp.
11h
reviewed Approve suggested edit on prime-constellations 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
comment Are semigroups with finite-to-one right multiplication “moving”?
I suppose right cancellative can be replaced by a uniform bound on the degree of finite-to-oneness.
Apr
21
comment Polytopes generated as the convex hull of the orbit of a finite reflection group acting on a given vector
Look for W-permutohedra or Coxeter group and permutohedra.
Apr
17
comment Computational complexity of deciding isomorphism of rational polyhedral cones
This is the tricky part to do in a way with reasonable complexity.
Apr
15
comment Schreier's index formula
Free pro-solvable groups and free pro-p groups satisfy Schreier's formula.
Apr
15
comment Schreier's index formula
@HJRW, this is why I hedged to the rf case.
Apr
14
comment Schreier's index formula
The intersection of all the terms of the derived series is trivial because the free group is residually a finite p-group and hence residually solvable. So you do get a free group and there is no contradiction.
Apr
14
comment 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
comment 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
comment Schreier's index formula
Let me hedge and assume the group is residually finite.
Apr
14
comment 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 pro-p analogue.
Apr
14
comment 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
comment 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 www-math.mit.edu/~apost/papers/permutohedron.pdf
Apr
8
comment automorphism of finitly generated group
Inna Bumagin and Daniel Wise proved it. sciencedirect.com/science/article/pii/S0022404904003111
Apr
8
comment automorphism of finitly generated group
It need not be finitely generated. Any countable group is the outer automorphism group of a fg group.