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Let $Z_{2^{\infty}}$ be 2-prufer group. I want to define $G=Z_{2^{\infty}}\ltimes b=<a,b|b^2=1,b^{-1}ab=a^{-1}$for $a\in="" a="">$ in sage. I think this is possible in GAP but I don't know how to define?

Let $Z_{2^{\infty}}$ $Z_{2^\infty}$ be 2-prufer group. I want to define $G=Z_{2^{\infty}}\ltimes $G=Z_{2^\infty}\ltimes b=<a,b|b^2=1,b^{-1}ab=a^{-1}$for$a\in="" a="">$ in sage. I think this is possible in GAP but I don't know how to define?

Let $Z_{2^\infty}$ $Z_{2^{\infty}}$ be 2-prufer group. I want to define $G=Z_{2^\infty}\ltimes b=<a,b|b^2=1,b^{-1}ab=a^{-1}$for $a\in="" a="">$ $G=Z_{2^{\infty}}$semi-direct $b$ =$<$$a$$,b|b^2=1,b^{-1}ab=a^{-1}$, for $a$ $\in A>$ in sage. I think this is possible in GAP but I don't know how to define?