Is SU(3) always contains SU(2) groups?

[Ans]

Hi,

I trying to understand. If there is non-trivial SU(3) group, is it always possible to find SU(2) as part of SU(3)?
And same question about SU(2) and U(1).

 

[Paul Colby]

Sure, there are many $SU(2)$ subgroups of $SU(3)$ just like there are many $O(2)$ subgroups of $O(3)$.

 

[Ans]

Thanks.

And another question about same.
SU(3) seems as have less number of parameters than SU(3)xSU(2)xU(1).
If there is SU(3) group, is is possible to say it is compatible with SU(3)xSU(2)xU(1) because SU(3) always contains SU(2) subgroups, and SU(2) always contains U(1)?

 

[Paul Colby]

The group, $G_1\times G_2$ is the tensor product of two independent groups. $G_1$ is contained in $G_1\times G_2$ by the projection $\pi : (g1,g2)\rightarrow g1$. The subgroup inclusion discussed in my previous reply is a subgroup of a different sort. (Mathematics is not my strongest subject) It would help to know what you mean by "compatible?"