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For n players, n-1 games are needed to fairly determine first place, and n-1+lg(n-1) are needed to fairly determine first and second place.

If a Sylow 2-subgroup T of G lies in a unique maximal 2-local P of G, then P is a "strongly embedded" subgroup of G, and G is known.

A graded algebra over the integers Z. Cohomology of a space is a graded ring.

The multiplicity of a multigraph is its maximum edge multiplicity.

A section of a graph obtained by finding its intersection with a plane.

An element of order 2 in a group (i.e., an element A of a group such that A^2=I, where I is the identity element).

The integral associated with the Haar measure.

The sporadic group HJ, also denoted J_2.

Related to one another by a homomorphism.

A connection between two or more vertices of a hypergraph. A hyperedge connecting just two vertices is simply a usual graph edge.