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A (Z)-group is a group faithfully represented as a doubly transitive permutation group in which no non-identity element fixes more than two points. A (ZT)-group is a (Z)-group that is of odd degree and not a Frobenius group , that is a Zassenhaus group of odd degree, also known as one of the groups PSL(2,2 k +1 ) or Sz(2 2 k +1 ) , for k any ...
V is the symmetry group of this cross: flipping it horizontally (a) or vertically (b) or both (ab) leaves it unchanged.A quarter-turn changes it. In two dimensions, the Klein four-group is the symmetry group of a rhombus and of rectangles that are not squares, the four elements being the identity, the vertical reflection, the horizontal reflection, and a 180° rotation.
Small groups of prime power order p n are given as follows: 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.
Z2 may refer to: Z2 (computer), a computer created by Konrad Zuse; Z2 (company), video game developer; Z2 Comics, a publisher of graphic novels, the quotient ring of the ring of integers modulo the ideal of even numbers, alternatively denoted by / Z 2, the cyclic group of order 2
This article gives a table of some common Lie groups and their associated Lie algebras.. The following are noted: the topological properties of the group (dimension; connectedness; compactness; the nature of the fundamental group; and whether or not they are simply connected) as well as on their algebraic properties (abelian; simple; semisimple).
The kth homology group is = / +, the s are the boundary maps of the simplicial complex and the rank of H k is the kth Betti number. Equivalently, one can define it as the vector space dimension of H k ( X ; Q ) since the homology group in this case is a vector space over Q .
Z² (short for Ziltoid 2; pronounced "zed squared" or alternatively "zee two" [5]) is a double album by Canadian musician Devin Townsend and his musical project Devin Townsend Project, [6] released on October 27, 2014. [7]
Groups whose lattice of subgroups is a complemented lattice are called complemented groups (Zacher 1953), and groups whose lattice of subgroups are modular lattices are called Iwasawa groups or modular groups (Iwasawa 1941). Lattice-theoretic characterizations of this type also exist for solvable groups and perfect groups (Suzuki 1951).