Generating finite completely reducible linear groups
Generating finite completely reducible linear groups
It is proved here that each finite completely reducible linear group of dimension <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="d"> <mml:semantics> <mml:mi>d</mml:mi> <mml:annotation encoding="application/x-tex">d</mml:annotation> </mml:semantics> </mml:math> </inline-formula> (over an arbitrary field) can be generated by <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left floor three halves d right floor"> <mml:semantics> <mml:mrow> <mml:mo>⌊</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mfrac> …