Novikov proved that the word problem for these objects is sometimes undecidable. Special types of these are called periodic or torsion ones, which are the subject of Burnside's problem. The Cayley graph is a method of representing these, and another one of these can be represented as a 194-by-194 character table, the Fischer-Greiss Monster. They may act on a set, usually as what may be called "symmetries" of that set, and functions from one to an
Novikov proved that the word problem for these objects is sometimes undecidable. Special types of these are called periodic or torsion ones, which are the subject of Burnside's problem. The Cayley graph is a method of representing these, and another one of these can be represented as a 194-by-194 character table, the Fischer-Greiss Monster. They may act on a set, usually as what may be called "symmetries" of that set, and functions from one to another that preserve their structure are called homomorphisms. Characterized by closure, associativity, and inverses, those that are commutative are also called abelian. FTP, name these algebraic structures, distinct from rings and fields.
Novikov proved that the word problem for these objects is sometimes undecidable.
Groups