Zobrazeno 1 - 10
of 501
pro vyhledávání: '"Tiep Pham"'
We determine the finite groups whose real irreducible representations have different degrees.
Comment: 16 pages, comments welcome
Comment: 16 pages, comments welcome
Externí odkaz:
http://arxiv.org/abs/2407.20854
We prove two results on some special generators of finite simple groups and use them to prove that every non-abelian finite simple group $S$ admits a non-congruence presentation (as conjectured in [CLT24]), and that if $S$ has a non-trivial Schur mul
Externí odkaz:
http://arxiv.org/abs/2407.19047
We obtain sharp bounds on the convergence rate of Markov chains on irreducible representations of finite general linear, unitary, and symplectic groups (in both odd and even characteristic) given by tensoring with Weil representations.
Comment:
Comment:
Externí odkaz:
http://arxiv.org/abs/2407.12713
Let $\Gamma$ be a cocompact, oriented Fuchsian group which is not on an explicit finite list of possible exceptions and $q$ a sufficiently large prime power not divisible by the order of any non-trivial torsion element of $\Gamma$. Then $|\mathrm{Hom
Externí odkaz:
http://arxiv.org/abs/2407.07193
Autor:
Guralnick, Robert M., Tiep, Pham Huu
We extend Gow's theorem on products of semisimple regular conjugacy classes to finite groups whose generalized Fitting subgroup is Z(G)S where S is a quasisimple group of Lie type in characteristic p and Z(G) has order prime to p.
Comment: 7 pag
Comment: 7 pag
Externí odkaz:
http://arxiv.org/abs/2404.05986
Autor:
Larsen, Michael, Tiep, Pham Huu
We prove that every simple unitary group $S$ of sufficiently large order satisfies Thompson's conjecture, that is, $S$ contains a conjugacy class $C$ such that $C^2 = S$. The proof relies on exponential character bounds recently obtained in arXiv:170
Externí odkaz:
http://arxiv.org/abs/2403.09047
Autor:
Larsen, Michael, Tiep, Pham Huu
For every finite quasisimple group of Lie type $G$, every irreducible character $\chi$ of $G$, and every element $g$ of $G$, we give an exponential upper bound for the character ratio $|\chi(g)|/\chi(1)$ with exponent linear in $\log_{|G|} |g^G|$, or
Externí odkaz:
http://arxiv.org/abs/2403.09046
In this paper we describe how to explicitly construct infinitely many finite simple groups as characteristic quotients of the rank 2 free group $F_2$. This shows that a "baby" version of the Wiegold conjecture fails for $F_2$, and provides counterexa
Externí odkaz:
http://arxiv.org/abs/2308.14302
Autor:
Larsen, Michael J., Tiep, Pham Huu
We extend to alternating groups $A_n$ several results about symmetric groups asserting that under various conditions on a conjugacy class, or more generally, a normal subset, $C$ of $S_n$, we have $C^2 \supseteq A_n\setminus\{1\}$
Comment: 13 pa
Comment: 13 pa
Externí odkaz:
http://arxiv.org/abs/2305.04806
We determine what are the fields of values of the irreducible $p$-height zero characters of all finite groups for $p=2$; we conjecture what they should be for odd primes, and reduce this statement to a problem on blocks of quasi-simple groups.
Externí odkaz:
http://arxiv.org/abs/2304.12869