Polynomial-Time Versions of Sylow's Theorem

FUZZY QUASI-METRIC VERSIONS OF A THEOREM OF GREGORI AND SAPENA

We provide fuzzy quasi-metric versions of a fixed point theorem ofGregori and Sapena for fuzzy contractive mappings in G-complete fuzzy metricspaces and apply the results to obtain fixed points for contractive mappingsin the domain of words.

A Formal Proof of Sylow's Theorem An Experiment in Abstract Algebra with Isabelle HOL

The theorem of Sylow is proved in Isabelle HOL. We follow the proof by Wielandt that is more general than the original and uses a non-trivial combinatorial identity. The mathematical proof is explained in some detail leading on to the mechanization of group theory and the necessary combinatorics in Isabelle. We present the mechanization of the proof in detail giving reference to theorems contai...

Sylow's Theorem in Polynomial Time

Given a set r of permutations of an n-set, let G be the group of permutations generated by f. If p is a prime, a Sylow p-subgroup of G is a subgroup whose order is the largest power of p dividing IGI. For more than 100 years it has been known that a Sylow p-subgroup exists, and that for any two Sylow p-subgroups PI, P, of G there is an element go G such that Pz = g-‘PI g. We present polynomial-...

Cauchy's Theorem and Sylow's Theorem from the Cyclic Case

We give a simultaneous proof of Cauchy’s theorem and Sylow’s theorem by reducing to the case of cyclic groups.

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials