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In MAGMA, if you are dealing with an element $x\in H$ for some group $H$, and you know that $H<G$ for some group $G$, is there an easy way to coerce $x$ into $G$ (e.g. if $H=\text{Alt}(n)$ and $G=\text{Alt}(n+k)$ for some $k\geq 1$)? The natural coercion method $G!x$ does not seem to work.

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I think holding someone over magma is probably a good method of coercion. (Apologies for the nonconstructive comment, but I couldn't resist.) –  Cameron Buie Nov 2 '12 at 9:14
    
Why didn't I think of that! –  David Ward Nov 2 '12 at 9:19
    
Sorry that is my mistake for using the worng MAGMA tag! Many apologese. –  David Ward Nov 2 '12 at 10:33
    
No need to apologize; after all, the correct tag didn't even exist when you asked this question. –  Ilmari Karonen Nov 2 '12 at 10:38
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2 Answers

up vote 3 down vote accepted

G!CycleDecomposition(g);

will work

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Thanks for the quick and helpful responses. –  David Ward Nov 2 '12 at 10:36
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One way would be to define the inclusion homomorphism $H \hookrightarrow G$ and apply it to your element $x$. See http://magma.maths.usyd.edu.au/magma/handbook/text/547#5783 for how to define homomorphisms.

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