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Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these.
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Isomorphic but non-conjugate subgroups of $GL(n,\mathbb{Z})$ ?
The answer to all three questions is yes and certainly is classical.
One simple example is the following:
Let $C_2$ act faithfully on the set $\{1,2,3,4\}$ in two ways. In the first the non-trivia …