Please Subscribe here, thank you!!! goo.gl/JQ8Nys The Klein Four-Group is the smallest noncyclic abelian group. Every proper subgroup is cyclic. We look at the the multiplication in the Klein Four-Group and find all of it's subgroups.
Good video. The Klein 4 group can be generated by the set of 180-degree rotations about the axes x,y, and z in three dimensional space. While the Klein 4 group is finite and commutative, the group of rotations is infinite and non-commutative. Is the group generated by the standard quaternion basis the same as the group generated by 90-degree rotations about the x, y, and z axes?
The German word "vier" (meaning 4) rhymes with the English "deer". Just put an "f" infront. Very similar words are also: - fear (tone down the a) - fierce (stop before the z loud)
of the klein 4? no it's not, remember H is a proper subgroup of G if H is a subgroup and H != G. So is a subgroup of the klein 4, but it's not the whole group ,so it's proper
@@TheMathSorcerer as far as I know If H is a subgroup of G and H=G or H= singleton set of identity element, then it's improper subgroup ... And here (e) is Identity ,so it's improper subgroup. Plz correct me if i am wrong..
Some authors of books use that as the definition. Depends on the books . I think it's more common to exclude the set with just the identity as this way the definition agrees with the set definition of a proper subset.
Is there an infinite set like the final Klein quartet? Please reply ... because I looked at this topic and I came with a group like the Klein Group, but it is not final. I want you to help me publish this paper.
I do not have a link ...but i have this paper ...I wrote this paper myself ... I searched a lot on the Internet and I didn't find it like that ... I want to show it to a professor who specializes in abstract mathematics now!
+The Math Sorcerer I really don't know why there are only 17 likes, this video is amazing, and all the work you did on Abstract Algebra is enormous and extremely valuable. Thank you very much! I have an exam tomorrow and I am revising using your videos. Thank you again!
