On the non-triviality of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>G</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>D</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> and the existence of maximal subgroups of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"><mml:msub><mml:mi mathvariant="italic">GL</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>D</mml:…