Finite groups

In group theory, a discipline within mathematics, a sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups.

In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.

In abstract algebra, a finite group is a mathematical group with a finite number of elements.

In modular arithmetic the set of congruence classes relatively prime to the modulus number, say n, form a group under multiplication called the multiplicative group of integers modulo n.

This lists the character tables for the more common molecular point groups used in the study of molecular symmetry.

In mathematical finite group theory, an N-group is a group all of whose local subgroups (that is, the normalizers of nontrivial p-subgroups) are solvable groups.

In finite group theory, a p-stable group for an odd prime p is a finite group satisfying a technical condition introduced by Gorenstein and Walter (, p.169, ) in order to extend Thompson's uniqueness results in the odd order theorem to groups with dihedral Sylow 2-subgroups.

In mathematics, the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups.

In mathematics, the Klein four-group (or just Klein group or Vierergruppe (English: four-group), often symbolized by the letter V or as K4) is the group Z2 × Z2, the direct product of two copies of the cyclic group of order 2.

In mathematics, an alternating group is the group of even permutations of a finite set.

In abstract algebra, the symmetric group Sn on a finite set of n symbols is the group whose elements are all the permutation operations that can be performed on n distinct symbols, and whose group operation is the composition of such permutation operations, which are defined as bijective functions from the set of symbols to itself.

In mathematics, physics and chemistry, a space group is the symmetry group of a configuration in space, usually in three dimensions.

In mathematical finite group theory, the trichotomy theorem divides the simple groups of characteristic 2 type and rank at least 3 into three classes.