bio | website | users.mct.open.ac.uk/ng3636 |
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location | Bristol | |
age | 37 | |
visits | member for | 4 years, 6 months |
seen | Apr 12 at 2:04 | |
stats | profile views | 1,406 |
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 |