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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.
| 1 | { |
| 2 | "domain": "mathematics", |
| 3 | "topics": [ |
| 4 | "algebra" |
| 5 | ], |
| 6 | "type": "proof", |
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| 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 | } |
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