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The Janko groups are the four sporadic groups J_1, J_2, J_3 and J_4. The Janko group J_2 is also known as the Hall-Janko group. The Janko groups are implemented in the ...

The Fischer groups are the three sporadic groups Fi_(22), Fi_(23), and Fi_(24)^'. These groups were discovered during the investigation of 3-transposition groups. The Fischer ...

The wallpaper groups are the 17 possible plane symmetry groups. They are commonly represented using Hermann-Mauguin-like symbols or in orbifold notation (Zwillinger 1995, p. ...

A finite simple group of Lie-type. The following table summarizes the types of twisted Chevalley groups and their respective orders. In the table, q denotes a prime power and ...

The classification theorem of finite simple groups, also known as the "enormous theorem," which states that the finite simple groups can be classified completely into 1. ...

The four following types of groups, 1. linear groups, 2. orthogonal groups, 3. symplectic groups, and 4. unitary groups, which were studied before more exotic types of groups ...

The five Mathieu groups M_(11), M_(12), M_(22), M_(23), and M_(24) were the first sporadic groups discovered, having been found in 1861 and 1873 by Mathieu. Frobenius showed ...

A point which lies on at least one ordinary line is called an ordinary point, or sometimes a regular point.

A point at the intersection of two or more grid lines in a point lattice.

A point which is a member of the set closure of a given set S and the set closure of its complement set. If A is a subset of R^n, then a point x in R^n is a boundary point of ...