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How many members are in these groups?

Anonymous Tue 10 Aug 02:05:21 2021 No.13497251 View Reply Original Report

Quoted By: >>13497290 >>13497364

How many members are in the $SU(2)$ group, and how many members are in the direct product of two groups (specifically $SU(2) \times SU(1)$ )?
Please provide your source so I know you're not trolling.

Anonymous

Anonymous Tue 10 Aug 2021 02:12:14 No.13497290 Report

Quoted By: >>13497364

>>13497251
I just realized that since $SU(1)$ only has one element $SU(2) \times SU(1)$ just has the same number of elements that $SU(2)$ has. Does the direct product of groups that have $a$ and $b$ members have $ab$ members?

Anonymous

Anonymous Tue 10 Aug 2021 02:31:47 No.13497364 Report

Quoted By:

>>13497251
$SU(1)$ is literally just $\{1\}$ . $SU(2)$ is a smooth topological manifold, so its cardinality is that of the reals.
>>13497290
For finite groups yes. This has nothing to do with groups and is just how direct (Cartesian) products of sets are defined, $X \times Y := \{ (x, y) \mid x \in X, y \in Y \}.$ Clearly the number of such ordered pairs $(x, y)$ is just $|X||Y|$ .

I don't have a source to provide, this is basic shit you can find in the first chapter of any book on the subjects. Or just look it up on wikipedia. Also next time use >>>/sci/sqt/

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