Some corollaries of Frobenius’ normal $p$-complement theorem

Frobenius’ Theorem

Given a manifold M of dimension n + k, attach to every p ∈ M an ndimensional subspace of the tangent space Tp(M). It is natural to ask if this collection of subspaces is the collection of tangent spaces to a family of submanifolds that cover M . In this paper we prove Frobenius’ Theorem, which gives a necessary and sufficient condition for the answer to be yes.

Frobenius kernel and Wedderburn's little theorem

We give a new proof of the well known Wedderburn's little theorem (1905) that a finite‎ ‎division ring is commutative‎. ‎We apply the concept of Frobenius kernel in Frobenius representation theorem in finite group‎ ‎theory to build a proof‎.

Stochastic Nonlinear Perron-frobenius Theorem∗

We establish a stochastic nonlinear analogue of the PerronFrobenius theorem on eigenvalues and eigenvectors of positive matrices. The result is formulated in terms of an automorphism T of a probability space (Ω,F , P ) and a random mapping D(ω, ·) : R+ → R+. Under assumptions of monotonicity and homogeneity of D(ω, ·), we prove the existence of scalar and vector measurable functions α(ω) > 0 an...

Cauchy ’ s theorem , Cauchy ’ s formula , corollaries Paul

frobenius kernel and wedderburn's little theorem

we give a new proof of the well known wedderburn's little theorem (1905) that a finite‎ ‎division ring is commutative‎. ‎we apply the concept of frobenius kernel in frobenius representation theorem in finite group‎ ‎theory to build a proof‎.