4,474 reputation
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bio website users.mct.open.ac.uk/ng3636
location Bristol
age 37
visits member for 4 years, 6 months
seen Apr 12 at 2:04
I'm a postdoc at the Open University.

Apr
2
revised Multiply transitive groups, continued
added first bullet
Mar
25
revised Multiply transitive groups, continued
forgot to include both of Arturo's results.
Mar
25
answered Multiply transitive groups, continued
Mar
24
comment Multiply transitive groups, continued
... There are also some classical results of Bocherdt, Manning and others, that directly bear on this. They give the conclusion you seek but require extra conditions, namely the presence of an element 'of small support'. (The ancestor of these kinds of results is Jordan's classification of primitive groups containing a 3-cycle.)... I can write down references if you want.
Mar
24
comment Multiply transitive groups, continued
... Of course the Schreier Conjecture is, as far as anyone can tell, impossibly difficult. (It asserts that the outer automorphism group of a finite simple group is solvable.)...
Mar
24
comment Multiply transitive groups, continued
This is most definitely not known - it would be a huge deal in finite group theory if it were. One way to solve this problem would be to prove the Schreier Conjecture, since Wielandt has shown that, given the Schreier Conjecture, any 7-transitive group contains $A_n$. You might be interested in this - dropbox.com/s/7abiro0h13jndob/Neumann%20on%20Wielandt.pdf - where Peter Neumann takes one paragraph to outline a weak version of Wielandt's argument which gives the result for 8-transitive rather than 7-transitive...
Mar
22
revised About structure of parabolic subgroups of finite classical algebraic groups
added 181 characters in body
Mar
22
comment About structure of parabolic subgroups of finite classical algebraic groups
Jim, I din't view your answer as undercutting mine at all! Mine was, in the first instance, idle speculation, and yours was a specific counterexample which was just what was needed. Although the original question is dealt with, I'm still interested about the minimality of the centre (from idle curiosity, nothing more).
Mar
21
revised About structure of parabolic subgroups of finite classical algebraic groups
added 282 characters in body
Mar
21
comment About structure of parabolic subgroups of finite classical algebraic groups
in your counterexample you have $Z(U)$ as a minimal normal subgroup, as I suggested would happen in my answer. I guess the original question could be reposed to ask whether $Z(U)$ is always minimal normal, i.e. whether a Levi always acts irreducibly on $Z(U)$? I imagine that there will be exceptions for small fields in special cases, but I wonder if this is true most of the time?
Mar
21
answered About structure of parabolic subgroups of finite classical algebraic groups
Mar
21
comment What is exceptional about the prime numbers 2 and 3?
The lovely paper by Doyle and Conway called Division by three - arxiv.org/abs/math/0605779 - explains why in the situation they consider (trying to divide infinite sets without the axiom of choice), the prime 2 is exceptional.
Mar
18
comment Find finite groups $G\cong Aut(G)$
should the word pseudocomplete in the second line be quasicomplete? Nice answer by the way. I have absolutely no idea how to answer your question!
Mar
11
comment List of Conjugacy Classes of the General Linear group over $\mathbb{Z}/p^2\mathbb{Z}$
@Gwyn, I think Steven Sam's blogpost only covers conjugacy classes for $GL_2(q)$, i.e. over a finite field. It seems like the MO knows this theory, but is unclear how to lift to the ring $Z/p^2Z$.... I might be wrong!
Mar
11
answered List of Conjugacy Classes of the General Linear group over $\mathbb{Z}/p^2\mathbb{Z}$
Mar
11
comment List of Conjugacy Classes of the General Linear group over $\mathbb{Z}/p^2\mathbb{Z}$
@Tobias, I edited the title to reflect your comment.
Mar
11
revised List of Conjugacy Classes of the General Linear group over $\mathbb{Z}/p^2\mathbb{Z}$
I edited the title in accordance with Tobias' comment
Mar
6
awarded  Popular Question
Feb
19
awarded  Necromancer
Feb
3
reviewed Edit suggested edit on Bordism and complex $K$-theory