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In this paper we will show how to generate in general A2n+1 and S2n+1 using a copy ofSn and an element of order 2 in A2n+1 or S2n+1 for all positive integers n≥2. We will also show how togenerate A2n+1 and S2n+1 symmetrically using n elements each of order 2

international journal of mathematics and mathematical sciences

Symmetric generating set of the groups<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$A_{2n + 1}$"><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mn>2</mml:mn><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="$S_{2n + 1}$"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>using<mml:…

Symmetric generating set of the groupsA2n+1andS2n+1using