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A subgroup is a subset H of group elements of a group G that satisfies the four group requirements. It must therefore contain the identity element. "H is a subgroup of G" is ...

An anyon is a projective representation of a Lie group.

The logarithmic distribution is a continuous distribution for a variate X in [a,b] with probability function P(x)=(lnx)/(b(lnb-1)-a(lna-1)) (1) and distribution function ...

Let G be a group with normal series (A_0, A_1, ..., A_r). A normal factor of G is a quotient group A_(k+1)/A_k for some index k<r. G is a solvable group iff all normal ...

The identity element of an additive group G, usually denoted 0. In the additive group of vectors, the additive identity is the zero vector 0, in the additive group of ...

The commutator subgroup (also called a derived group) of a group G is the subgroup generated by the commutators of its elements, and is commonly denoted G^' or [G,G]. It is ...

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

If a matrix group is reducible, then it is completely reducible, i.e., if the matrix group is equivalent to the matrix group in which every matrix has the reduced form ...

Given three curves phi_1, phi_2, phi_3 with the common group of ordinary points G (which may be empty), let their remaining groups of intersections g_(23), g_(31), and g_(12) ...

A homogeneous space M is a space with a transitive group action by a Lie group. Because a transitive group action implies that there is only one group orbit, M is isomorphic ...