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In this paper we will show how to generate Akn+1 and 	Skn+1 using a copy of Sn and an element of order k in Akn+1 and Skn+1 respectively, for all positive integers n≥2 and all positive integers k≥2. We will also show how to generate Akn+1 and  Skn+1 symmetrically using nelements each of order k, for all n≥2 and all even integers k≥2

international journal of mathematics and mathematical sciences

Symmetric and permutational generating set of the groups<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$A_{kn+1}$"><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$S_{kn+1}$"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:…

Symmetric and permutational generating set of the groupsAkn+1andSkn+1