منابع مشابه
on finite arithmetic groups
let $f$ be a finite extension of $bbb q$, ${bbb q}_p$ or a global field of positive characteristic, and let $e/f$ be a galois extension. we study the realization fields of finite subgroups $g$ of $gl_n(e)$ stable under the natural operation of the galois group of $e/f$. though for sufficiently large $n$ and a fixed algebraic number field $f$ every its finite extension $e$ is re...
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We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic groups. We also construc...
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We study testing properties of functions on finite groups. First we consider functions of the form f : G → C, where G is a finite group. We show that conjugate invariance, homomorphism, and the property of being proportional to an irreducible character is testable with a constant number of queries to f , where a character is a crucial notion in representation theory. Our proof relies on represe...
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Brown and Buhler [ 3 ] and F rank l , G r a h a m and R6dl [ 4 ] p roved tha t D(G) = o(IG I) for all G (here, and t h r o u g h o u t the pape r G denotes a finite abe l ian g roup of odd order) . In this no te we are in teres ted in D(G) for g roups with m a n y const i tuents . A lon and D u b i n e r [ 1, 2] asked whether there exists a cons tan t c < 3 such tha t D(Z~)~<c". I. Ruzsa has re...
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For positive integers n and k, the anti-van der Waerden number of Zn, denoted by aw(Zn, k), is the minimum number of colors needed to color the elements of the cyclic group of order n and guarantee there is a rainbow arithmetic progression of length k. Butler et al. showed a reduction formula for aw(Zn, 3) = 3 in terms of the prime divisors of n. In this paper, we analagously define the anti-va...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2007
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700038971