Abstract Algebra | The quaternion group

We present the quaternion group. This is an important example of a non-abelian group of small order.

[shazlynassar]

How the arithmetic operations addition, subtraction, multiplication and division are performed within that group?

[ronycb]

Hey just also wanted to say that I checked out your description and saw Randolph College over there. It's people like you who Make America Great and also make me wanna study there at least, if not live there... ❤🇺🇲🙏🏼

[ronycb]

Also I think there's a matrix way to represent these types of complex numbers and the quaternion group, would be glad if somebody helped me out 😅😅

[fuseteam]

Here's another mnemonic
I=jk (i am joking)

[ashishKjr]

This also disproves the converse of the following fact: Every subgroup of an abelian group is normal. It's quite a cool group!

[yondabigman]

I feel happy that I can understand a maths video for once

[ronycb]

I'm sorry but I referred your real analysis playlist for my distance ie open course and I just wanted to say thanks by contributing sth to say you really do mean something to me. That is worth sth at least where I live at least well a pack of cigarettes and yes I do smoke nowadays long story but not encouraging it to anyone who is not on really really on the verge of suicide

[zzane]

Could I get a clarification on something? For i, j, and k are we supposed to treat them like a complex number or basis vector? The cyclic subgroups look to me like powers of complex numbers but I've normally heard of quaternions described as a 4d vector space with a vector part and scalar part.

[OMGclueless]

Question about showing (-i)^2 = -1. You wrote (-i)^2 = (-i)(-i) = (-1)^2 i^2. But doesn't that last step involve commuting i and -1, which is not necessarily allowed in this group?

[inquistive]

great as always!! can u please post a video explaining what are primitive roots. u have made many videos related to primiitve roots.But I couldn't find one which explains what exactly primitive roots are . Thanks!!

[tenmiltenmil]

Huh …? Who invented this gibberish ?
🧐🧐🧐🤔🤔🤔🤨🤨🤨😡😡😡