CORDIS Project
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This project explores the mathematical properties of group words and their applications in various areas of mathematics. It aims to solve significant problems in group theory and related fields using a variety of mathematical techniques.
Hilbert's solution to Waring problem in Number Theory shows that every positive integer is a sum of g(n) nth powers.
Surprising non-commutative analogues of this phenomenon were discovered recently in Group Theory, where powers are replaced by general words.
Moreover, the study of group words occurs naturally in important contexts, such as the Burnside problems, Serre's problem on profinite groups, and finite simple group theory.
We propose a systematic study of word maps on groups, their images…
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