Frobenius automorphism

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• Automorphism — In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms… …   Wikipedia

• Frobenius group — In mathematics, a Frobenius group is a transitive permutation group on a finite set, such that no non trivial elementfixes more than one point and some non trivial element fixes a point. They are named after F. G. Frobenius. Structure The… …   Wikipedia

• Frobenius endomorphism — In commutative algebra and field theory, which are branches of mathematics, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of rings with prime characteristic p , a class importantly including fields. The… …   Wikipedia

• Arithmetic and geometric Frobenius — In mathematics, the Frobenius endomorphism is defined in any commutative ring R that has characteristic p , where p is a prime number. Namely, the mapping φ that takes r in R to r p is a ring endomorphism of R .The image of φ is then R p , the… …   Wikipedia

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