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A group G is quasi-unipotent if every element of G of order p is unipotent for all primes p such that G has p-group rank >=3.

The Ree group R(q) is the automorphism group of a S(2,q+1,q^3+1) Steiner system.

The Tits group is a group of order 17971200. It is implemented in the Wolfram Language as TitsGroupT[].

A group in which the elements are square matrices, the group multiplication law is matrix multiplication, and the group inverse is simply the matrix inverse. Every matrix ...

A proper subgroup is a proper subset H of group elements of a group G that satisfies the four group requirements. "H is a proper subgroup of G" is written H subset G. The ...

A normalizer of a nontrivial Sylow p-subgroup of a group G.

A group action G×X->X is transitive if it possesses only a single group orbit, i.e., for every pair of elements x and y, there is a group element g such that gx=y. In this ...

A hole in a mathematical object is a topological structure which prevents the object from being continuously shrunk to a point. When dealing with topological spaces, a ...

The homotopy groups generalize the fundamental group to maps from higher dimensional spheres, instead of from the circle. The nth homotopy group of a topological space X is ...

Let G be a subgroup of the modular group Gamma. Then an open subset R_G of the upper half-plane H is called a fundamental region of G if 1. No two distinct points of R_G are ...