Omega subgroups of pro - p groups ∗
نویسندگان
چکیده
Let G be a pro-p group and let k ≥ 1. If γk(p−1)(G) ≤ γr(G) s for some r and s such that k(p − 1) < r + s(p − 1), we prove that the exponent of Ωi(G) is at most pi+k−1 for all i.
منابع مشابه
A Subgroup Theorem for Free Products of Pro-Finite Groups
The notion of a free product of pro-finite groups has some important applications in the theory of algebraic number fields (see [3]). In this connection, it is interesting to get some knowledge about the subgroups of such a free product. The aim of this paper is to show a theorem for the open subgroups of a free pro-finite product, which is an analog of Kurosh’s wellknown subgroup theorem for t...
متن کاملProducts of absolute Galois groups ∗
If the absolute Galois group GK of a field K is a direct product GK = G1 × G2 then one of the factors is prosolvable and either G1 and G2 have coprime order or K is henselian and the direct product decomposition reflects the ramification structure of GK . So, typically, the direct product of two absolute Galois groups is not an absolute Galois group. In contrast, free (profinite) products of ab...
متن کاملEffects of aerobic training and omega-3 supplementation on the levels of CRP, MDA and lipid profile in overweight and obese women
Introduction: Exercise training and omega 3 supplements play an important role in modulating the levels of oxidative and inflammatory mediators. The present study conducted aimed to investigate the effects of aerobic training and omega-3 supplementation on the levels of oxidative (MDA) and inflammatory (CRP) mediators and lipid profile in overweight and obese women. Materials and Methods: The ...
متن کاملWhich groups are amenable to proving exponent two for matrix multiplication?
The Cohn-Umans group-theoretic approach to matrix multiplication suggests embedding matrix multiplication into group algebra multiplication, and bounding $\omega$ in terms of the representation theory of the host group. This framework is general enough to capture the best known upper bounds on $\omega$ and is conjectured to be powerful enough to prove $\omega = 2$, although finding a suitable g...
متن کاملIrreducible characters of Sylow $p$-subgroups of the Steinberg triality groups ${}^3D_4(p^{3m})$
Here we construct and count all ordinary irreducible characters of Sylow $p$-subgroups of the Steinberg triality groups ${}^3D_4(p^{3m})$.
متن کامل