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Elements inverted by an automorphism and the sum of character degrees
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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| 1 | +{ | |
| 2 | + "domain": "mathematics", | |
| 3 | + "topics": [ | |
| 4 | + "algebra" | |
| 5 | + ], | |
| 6 | + "type": "proof", | |
| 7 | + "also": [ | |
| 8 | + "construction" | |
| 9 | + ], | |
| 10 | + "source": { | |
| 11 | + "key": "kourovka", | |
| 12 | + "name": "The Kourovka Notebook", | |
| 13 | + "url": "https://kourovkanotebookorg.wordpress.com/wp-content/uploads/2026/10/21tkt-3.pdf#page=106", | |
| 14 | + "id": "16.60", | |
| 15 | + "curator": "E. I. Khukhro and V. D. Mazurov", | |
| 16 | + "poser": "D. MacHale", | |
| 17 | + "status": "unsolved; unverified AI solution proposed", | |
| 18 | + "as_of": "2026-10-20", | |
| 19 | + "catalog": "0521c19bbd38" | |
| 20 | + } | |
| 21 | +} | |