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bio website rwoodroofe.math.msstate.edu
location Starkville, MS
age
visits member for 2 years, 4 months
seen 2 days ago

Assistant Professor of Mathematics at Mississippi State University.


Apr
17
comment $2$-group with two isomorphic normal subgroups of index $4$ with non-isomorphic quotients
This question has a somewhat similar flavor to mathoverflow.net/questions/153433/…
Mar
30
comment Which graphs generate a matroidal independence complex?
My favorite example is the cross polytope (i.e., generalized octahedron), which is the independence complex of the disjoint union of $K_2$'s.
Mar
28
comment What have simplicial complexes ever done for graph theory?
MatouĊĦek's nice book "Using the Borsuk-Ulam theorem" should be mentioned here. It is a grad-student accessible, book-length treatment of the Lovász solution to the Kneser problem and more recent improvements (and all the background you need to understand them).
Mar
14
comment matroids axioms and independence system
@user47659: Yes, that's what I mean. It's easiest to prove if you focus on the (minimal) non-faces of $\Delta$ and the circuits of matroids, rather than the faces and independent sets. Here face == independent set, in different terminology.
Mar
12
answered matroids axioms and independence system
Feb
10
comment Classification of automorphism groups of groups of order $p^4$
Yes, StructureDescription is limited. But is there a better alternative for getting a human-readable description of groups, suitable for MathOverflow? (I guess one easy improvement would be to only ask for the structure of the outer automorphism group.)
Feb
10
answered Classification of automorphism groups of groups of order $p^4$
Feb
9
comment Classification of automorphism groups of groups of order $p^4$
It's not a complete answer to your question, but if you want to get some intuition, GAP (and hence SAGE) has a library of all groups of order $p^4$ built in. See gap-system.org/Packages/sgl.html
Feb
6
comment Iterated semi-direct products
Maybe the fact that Gaschütz's Theorem (see my answer below) doesn't hold when $C$ is not abelian will give a counterexample in this case? (But I didn't immediately find the counterexample, even without the cyclic constraints.)
Feb
5
comment Iterated semi-direct products
By the way, you can find (a slightly more general version of) Gaschütz's Theorem as Theorem 3.3.2 of "The theory of finite groups" by Kurzweil and Stellmacher. The result is very useful in situations like this question, and in my opinion it should be more widely known.
Feb
4
answered Iterated semi-direct products
Feb
4
comment Topological spaces made by identifying opposite faces of a cube?
Of course, if you do the same with a dodecahedron with the correct twist, you famously get the Poincare homology sphere! en.wikipedia.org/wiki/…
Feb
3
comment Is there an analog of Sperner's lemma for the Hopf invariant?
The relevant page of Hilton's text can be reached (at least for now) by Google Books at books.google.com/…
Feb
3
revised Is there an analog of Sperner's lemma for the Hopf invariant?
fixed typos, clarified language
Feb
3
comment Is there an analog of Sperner's lemma for the Hopf invariant?
If I'm understanding Hilton's formulation, I think it should suffice to take one such disc, corresponding with $f^{-1}$ of a single point. Of course, if $\Delta$ is sufficiently finely subdivided, it shouldn't matter what color you pick.
Feb
3
revised Is there an analog of Sperner's lemma for the Hopf invariant?
Fixed degree condition, expanded answer
Feb
1
answered Is there an analog of Sperner's lemma for the Hopf invariant?
Jan
31
comment Factor subset of finite group
No, I don't think maximal is necessary. Indeed, you might get a bit of extra power by looking also at meet-irreducible (but not necessarily maximal) subgroups.
Jan
29
answered Factor subset of finite group
Jan
28
comment Factor subset of finite group
Unless I'm mistaken, the same argument proves the statement for any group having a series of subgroups, each of prime index in the next. That takes care of e.g. $A_5$, and indeed any group with all composition factors either abelian or isomorphic to $A_5$.