In this paper, we characterize the unit groups of semisimple group algebras $\mathbb{F}_qG$ non-metabelian order $108$, where $F_q$ is a field with $q=p^k$ elements for some prime $p > 3$ and positive integer $k$. Up to isomorphism, there are $45$ $108$ but only $4$ them non-metabelian. We consider all find Wedderburn decomposition their algebras. And as by-product obtain groups.

in this paper, lie group structure and lie algebra structure of unit complex 3-sphere     are studied. in order to do this, adjoint representations of unit biquaternions (complexified quaternions) are obtained. also, a correspondence between the elements of     and the special complex unitary matrices    (2) is given by expressing biquaternions as 2-dimensional bicomplex numbers    .  the relat...