Rational linear groups with finitely many automorphism orbits
Show that a group of rational matrices with finitely many automorphism orbits is virtually soluble; check two proposed proofs.
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Show that a group of rational matrices with finitely many automorphism orbits is virtually soluble; check two proposed proofs.
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Find a finite p-group of odd order with exactly as many automorphisms as elements, or check the proposed example of order 1009^52359.
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Show that an automorphism of a finite group inverts at most as many elements as the sum of the irreducible character degrees.
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