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A measure that takes on real values.

A quadratic field Q(sqrt(D)) with D>0.

A relation R on a set S is reflexive provided that xRx for every x in S.

A reflexive relation.

A property of finite simple groups which is known for all such groups.

A p-element x of a group G is semisimple if E(C_G(x))!=1, where E(H) is the commuting product of all components of H and C_G(x) is the centralizer of G.

Theta(G;A)=<theta(a):a in A-1> is an A-invariant solvable p^'-subgroup of G.

Denoted sl_n.

A type II Markov move.

L is a subnormal subgroup of H if there is a "normal series" (in the sense of Jordan-Hölder) from L to H.