Search Results
Search type | Search syntax |
---|---|
Tags | [tag] |
Exact | "words here" |
Author |
user:1234 user:me (yours) |
Score |
score:3 (3+) score:0 (none) |
Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
Views | views:250 |
Code | code:"if (foo != bar)" |
Sections |
title:apples body:"apples oranges" |
URL | url:"*.example.com" |
Saves | in:saves |
Status |
closed:yes duplicate:no migrated:no wiki:no |
Types |
is:question is:answer |
Exclude |
-[tag] -apples |
For more details on advanced search visit our help page |
This tag is used if a reference is needed in a paper or textbook on a specific result.
9
votes
Accepted
Results about the existence of solutions in groups
If you are interested in finite simple groups, there is a whole raft of literature considering the related question of which words maps $w: G^n\to G$ are surjective. The answer is often yes, so this g …
3
votes
Accepted
Conjugacy classes in PSL(3,q) and PSU(3,q)
This is well-known, and there are a number of relevant references. Firstly, there are these by Wall (they are pretty hard to read though).
Wall, G. E. Conjugacy classes in projective and special line …
11
votes
3
answers
820
views
Finite groups with few conjugacy classes of maximal subgroups
Let $c$ be a positive integer, $G$ a finite group with at most $c$ conjugacy classes of maximal subgroup. What can we say about $G$?
Same question, but this time $G$ is a finite group with at most $ …
8
votes
Accepted
Finite groups factorized into two simple alternating groups
For $m=5$ and $n$ arbitrary, all factorizations are classified here:
W. R. Scott, Products of $A_5$ and a finite simple group, J. Algebra
37 (1975), 165--171.
For $m=6$ and $m=7$ (again with $ …
3
votes
Accepted
On Groups of Maximal Class: Reference
I believe the study of $p$-groups of maximal class really kicked off with this paper:
Blackburn, N.
On a special class of p-groups.
Acta Math. 100 1958 45–92.
These days the basic source is: …
17
votes
Accepted
Reference for the triple covering of A_6
The oval construction for $3\cdot A_6$ can be found on p.110 of
Symmetric Generation of Groups With Applications to Many of the Sporadic Finite
Simple Groups by Robert Curtis.
An e-version is …
4
votes
Subgroups of GL_2 over a finite field
Dickson is responsible for the classification of subgroups of $SL_2(\mathbb{F}_q)$ (and once you've got this the subgroups of $GL_2(\mathbb{F}_q)$ are easy). You can find a full proof in Suzuki's "Gro …
3
votes
0
answers
54
views
Cliques in Incomplete block designs
I'm interested in inequalities that guarantee the presence of cliques in incomplete block designs. Here's the set-up:
I have an incidence structure $(V, B)$ which is an incomplete block design: $V$ is …
7
votes
Realizable Order Sequences for Finite Groups
I don't know if this constitutes an answer but... You might be interested in the paper by Mazurov called The set of orders of elements in a finite group.
Given a group $G$, Mazurov defines $\omega(G …
5
votes
A family of skew-symmetric matrices corresponding to cycles in graphs
This isn't a proper answer, but it's slightly too long for a comment...
A matrix that satisfies (i) and (ii) is biregular and skew-symmetric. In principle a biregular skew-symmetric matrix could have …
10
votes
Measures of non-abelian-ness
For certain applications, the abelian-ness of a group is inversely proportional to the quasirandom-ness of a group. The latter notion is more obscure, so this observation might not be a help at first. …
7
votes
Letter from Grothendieck to Tate on "crystals"
I don't know if this is of any use.... but I believe that the ideas in this letter were written up somewhat later in this article:
Grothendieck, A.
Crystals and the de Rham cohomology of schemes …
7
votes
Accepted
Finite subgroups of $GL(2,K)$ with $K\neq\mathbb{C}$
An answer to your questions is provided by this article of Beauville:
Beauville, Arnaud, Finite subgroups of (\mathrm{PGL}_2(K))., García-Prada, Oscar (ed.) et al., Vector bundles and complex geometr …
2
votes
2
answers
305
views
Random walk and isoperimetric constant
I assume that a result of the following kind is known, and I would really appreciate a reference for it... Or at least, some hints as to where to start looking.
Theorem(?): Let $\varepsilon>0$ and …
9
votes
Maximal number of maximal subgroups
The document I linked to above is sufficiently striking as to warrant an answer of its own. I hope it complements the community wiki above.
As mentioned above the relevant conjecture in this area is …