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Abstract Excluding some exceptional cases, we determine the asphericity of the relative presentation ???? = 〈 G , x ∣ a x m b x n 〉… Click to show full abstract
Abstract Excluding some exceptional cases, we determine the asphericity of the relative presentation ???? = 〈 G , x ∣ a x m b x n 〉 {\mathcal{P}=\langle G,x\mid ax^{m}bx^{n}\rangle} , where a , b ∈ G ∖ { 1 } {a,b\in G\setminus\{1\}} and 1 ≤ m ≤ n {1\leq m\leq n} . If H = 〈 a , b 〉 ≤ G {H=\langle a,b\rangle\leq G} , the exceptional cases occur when a = b 2 {a=b^{2}} or when H is isomorphic to C 6 {C_{6}} .
Keywords:
positive free;
free product;
relative group;
asphericity positive;
length relative;
product length
Journal Title: Forum Mathematicum
Year Published: 2018
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Journal Title: Forum Mathematicum
Year Published: 2018
Link to full text (if available)
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recommendations!