Overview
A particular subgroup of the Lorentz group can be found by considering matrices of the form
{%
\begin{bmatrix}
1 & 0 \\
0 & R _{3x3}\\
\end{bmatrix}
%}
where {% R _{3x3} %} is the 3 dimensional
rotation group.
That is, rotations with no boost are acceptable Lorentz transformations, as can be seen by plugging them into the
defining equation for Lorentz transformations.
{% \Lambda ^T \eta \Lambda = \eta %}