Pseudo-reflection groups and essential dimension
نویسندگان
چکیده
منابع مشابه
Pseudo-reflection groups and essential dimension
We give a simple formula for the essential dimension of a finite pseudoreflection group at a prime p and determine the absolute essential dimension for most irreducible pseudo-reflection groups. We also study the “poor man’s essential dimension” of an arbitrary finite group, an intermediate notion between the absolute essential dimension and the essential dimension at a prime p.
متن کامل(∗)-groups and pseudo-bad groups
We give an example of an infinite simple Frobenius group G without involutions, with a trivial kernel and a nilpotent complement. Nevertheless, this group is not ωstable (not even superstable), this is the ”only” property missing in order to be a counterexample to the Cherlin-Zil’ber Conjecture which says that simple ωstable groups are algebraic groups.
متن کاملEssential Dimension and Canonical Dimension of Gerbes Banded by Groups of Multiplicative Type
We prove the formula ed(X ) = cdim(X ) + ed(A) for any gerbe X banded by an algebraic group A which is the kernel of a homomorphism of algebraic tori Q → S with Q invertible and S split. This result is applied to prove new results on the essential dimension of algebraic groups.
متن کاملEssential Dimension of Finite Groups in Prime Characteristic
Let F be a eld of characteristic p > 0 and G be a smooth nite algebraic group over F . We compute the essential dimension edF (G; p) of G at p. That is, we show that edF (G; p) = { 1, if p divides |G|, and 0, otherwise.
متن کاملOn the essential dimension of cyclic p - groups
Let p be a prime number and r ≥ 1 an integer. We compute the essential dimension of Z/pZ over fields of characteristic not p, containing the p-th roots of unity (theorem 3.1). In particular, we have edQ(Z/8Z) = 4, a result which was conjectured by Buhler and Reichstein in 1995 (unpublished).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2014
ISSN: 0024-6107
DOI: 10.1112/jlms/jdu056