In mathematics, the Klein four-group is an abelian group with four elements, in which each element is self-inverse (composing it with itself produces the...

Four group or Group of Four may refer to: Klein four-group Four note group G4 nations Lucky Four Group Clause Four Group Gang of Four (disambiguation)...

Christian Klein (German: [klaɪn]; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work in group theory,...

small groups for the cases n ≤ 8. The dihedral group of order 8 (D4) is the smallest example of a group that is not a T-group. Any of its two Klein four-group...

quotient group S 4 / K {\displaystyle \mathrm {S} _{4}/K} on the orbit of the cross-ratio. The four permutations in K make a realization of the Klein four-group...

group theory, a branch of mathematics, a subset of a group G is a subgroup of G if the members of that subset form a group with respect to the group operation...

uncountably many. The smallest non-cyclic group has four elements; it is the Klein four-group. An alternating groups are not simple for values n {\displaystyle...

and G' are isomorphic as groups. For instance, there are 8 {\displaystyle 8} inequivalent extensions of the Klein four-group by Z / 2 Z {\displaystyle...

/ Z ≅ S 1 {\displaystyle \mathbb {R} /\mathbb {Z} \cong S^{1}} The Klein four-group is isomorphic to the direct product of two copies of Z 2 = Z / 2 Z...

these two generators define a group of order 4 {\displaystyle 4} , the Klein four-group, they determine the entire Galois group. Another example is given...