If <mml:math alttext="$(G,\cdot)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>G</mml:mi><mml:mo>,</mml:mo><mml:mo>&#8901;</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> is a group with identity <mml:math alttext="$e$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>e</mml:mi></mml:math>, we call <mml:math alttext="$G$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>G</mml:mi></mml:math>, the group based at <mml:math alttext="$e$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>e</mml:mi></mml:math>. In this paper, we aim to release the present day group theory which is based at <mml:math alttext="$e$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>e</mml:mi></mml:math>, by replacing <mml:math alttext="$e$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>e</mml:mi></mml:math> by an arbitrary element of the group.

International Journal of Mathematics and Mathematical Sciences

Group theory based at any point

Abstract

Copyright