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The number of elements of a group in a given conjugacy class.

A type I Markov move.

A group of sociable numbers of order 3.

In the American system, 10^(33).

A sequence {a_1,a_2,...} for which a_1>=a_2>=....

An analytic, Borel, or coanalytic set.

The number q in a fraction p/q.

The difference of two numbers n_1 and n_2 is n_1-n_2, where the minus sign denotes subtraction.

For a finite group of h elements with an n_ith dimensional ith irreducible representation, sum_(i)n_i^2=h.

A simple graph with n>=3 graph vertices in which each graph vertex has vertex degree >=n/2 has a Hamiltonian cycle.