enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Cyclic group - Wikipedia

    en.wikipedia.org/wiki/Cyclic_group

    A cyclic group is a group which is equal to one of its cyclic subgroups: G = g for some element g, called a generator of G. For a finite cyclic group G of order n we have G = {e, g, g 2, ... , g n−1}, where e is the identity element and g i = g j whenever i ≡ j (mod n); in particular g n = g 0 = e, and g −1 = g n−1.

  3. List of small groups - Wikipedia

    en.wikipedia.org/wiki/List_of_small_groups

    Order p: The only group is cyclic. Order p 2: There are just two groups, both abelian. Order p 3: There are three abelian groups, and two non-abelian groups. One of the non-abelian groups is the semidirect product of a normal cyclic subgroup of order p 2 by a cyclic group of order p.

  4. List of finite simple groups - Wikipedia

    en.wikipedia.org/wiki/List_of_finite_simple_groups

    The order of the outer automorphism group is written as d⋅f⋅g, where d is the order of the group of "diagonal automorphisms", f is the order of the (cyclic) group of "field automorphisms" (generated by a Frobenius automorphism), and g is the order of the group of "graph automorphisms" (coming from automorphisms of the Dynkin diagram).

  5. Small Latin squares and quasigroups - Wikipedia

    en.wikipedia.org/wiki/Small_Latin_squares_and...

    Of the 161,280 Latin squares of order five, there are 56 reduced squares. There are two main classes and only two isotopy classes, but 1,411 isomorphism classes. There are six isomorphism classes that contain reduced squares, that is, there are six loops, only one of which is a group, the cyclic group of order five. [1]

  6. Cyclically ordered group - Wikipedia

    en.wikipedia.org/wiki/Cyclically_ordered_group

    Given a cyclically ordered group K and an ordered group L, the product K × L is a cyclically ordered group. In particular, if T is the circle group and L is an ordered group, then any subgroup of T × L is a cyclically ordered group. Moreover, every cyclically ordered group can be expressed as a subgroup of such a product with T. [3]

  7. Subgroups of cyclic groups - Wikipedia

    en.wikipedia.org/wiki/Subgroups_of_cyclic_groups

    [5] [6] [7] (See also cyclic group for some characterization.) There exist finite groups other than cyclic groups with the property that all proper subgroups are cyclic; the Klein group is an example. However, the Klein group has more than one subgroup of order 2, so it does not meet the conditions of the characterization.

  8. Classification of finite simple groups - Wikipedia

    en.wikipedia.org/wiki/Classification_of_finite...

    In mathematics, the classification of finite simple groups (popularly called the enormous theorem [1] [2]) is a result of group theory stating that every finite simple group is either cyclic, or alternating, or belongs to a broad infinite class called the groups of Lie type, or else it is one of twenty-six exceptions, called sporadic (the Tits group is sometimes regarded as a sporadic group ...

  9. Cycle graph (algebra) - Wikipedia

    en.wikipedia.org/wiki/Cycle_graph_(algebra)

    Cycle graph of the quaternion group Q 8. Cycles that contain a non-prime number of elements have cyclic subgroups that are not shown in the graph. For the group Dih 4 above, we could draw a line between a 2 and e since (a 2) 2 = e, but since a 2 is part of a larger cycle, this is not an edge of the cycle graph.