Let F be any field. Show that there is a 1-1 homormophism from to $GL(n,F)$ given by the action of on the indices i in the standard basis . Combine this with Cayley’s theorem (page 120) to show that for every finite group G, there exists n, such that G is isomorphic to a subgroup of .

Show algebraically that every isometry T of is a glide reflection provided it has the form $\latex T=T_\lambda A$, where $A\in O(2,R)$, $A\not\in SO(2,R)$, $\latex \lambda\ne 0$.

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