35.8k views
5 votes
What is the meaning of "Klein four-group (Viergruppe) V4"?

What is the meaning of "Klein four-group (Viergruppe) V4"?-example-1
User Warna
by
7.4k points

2 Answers

2 votes

Answer:

It was named Vierergruppe (meaning four-group) by Felix Klein in 1884. It is also called the Klein group, and is often symbolized by the letter V or as K4. The Klein four-group, with four elements, is the smallest group that is not a cyclic group.

User Odisseo
by
8.1k points
4 votes

The vierergruppe is the Abelian abstract group on four elements that is isomorphic to the finite group C2×C2 and the dihedral group. The multiplication table of one possible representation is illustrated below. It can be generated by the permutations 1, 2, 3, 4, 2, 1, 4, 3, 3, 4, 1, 2, and 4, 3, 2, 1.

User Unsparing
by
8.3k points