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1. CMB Online first
Characters on $C( X)$ The precise condition on a completely regular space $X$ for every character on
$C(X) $ to be an evaluation at some point in $X$ is that $X$ be
realcompact. Usually, this classical result is obtained relying heavily on
involved (and even nonconstructive) extension arguments. This note provides a
direct proof that is accessible to a large audience.
Keywords:characters, realcompact, evaluation, real-valued continuous functions Categories:54C30, 46E25 |
2. CMB Online first
ZL-amenability Constants of Finite Groups with Two Character Degrees We calculate the exact amenability constant of the centre of
$\ell^1(G)$ when $G$ is one of the following classes of finite group:
dihedral; extraspecial; or Frobenius with abelian complement and
kernel. This is done using a formula which applies to all finite
groups with two character degrees. In passing, we answer in the
negative a question raised in work of the third author with Azimifard
and Spronk (J. Funct. Anal. 2009).
Keywords:center of group algebras, characters, character degrees, amenability constant, Frobenius group, extraspecial groups Categories:43A20, 20C15 |
3. CMB 2013 (vol 57 pp. 125)
Camina Triples In this paper, we study Camina triples. Camina triples are a
generalization of Camina pairs. Camina pairs were first introduced
in 1978 by A .R. Camina.
Camina's work
was inspired by the study of Frobenius groups. We
show that if $(G,N,M)$ is a Camina triple, then either $G/N$ is a
$p$-group, or $M$ is abelian, or $M$ has a non-trivial nilpotent or
Frobenius quotient.
Keywords:Camina triples, Camina pairs, nilpotent groups, vanishing off subgroup, irreducible characters, solvable groups Category:20D15 |
4. CMB 2013 (vol 57 pp. 9)
Integral Sets and the Center of a Finite Group We give a description of the atoms in the Boolean algebra generated by the integral subsets of a finite group.
Keywords:integral set, characters, Boolean algebra Category:20C99 |
5. CMB 2002 (vol 45 pp. 337)
Surjectivity of $\mod\ell$ Representations Attached to Elliptic Curves and Congruence Primes For a modular elliptic curve $E/\mathbb{Q}$, we show a number of
links between the primes $\ell$ for which the mod $\ell$
representation of $E/\mathbb{Q}$ has projective dihedral image and
congruence primes for the newform associated to $E/\mathbb{Q}$.
Keywords:torsion points of elliptic curves, Galois representations, congruence primes, Serre tori, grossencharacters, non-split Cartan Categories:11G05, 11F80 |