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Odd-order p-groups with as many automorphisms as elements
Find a finite p-group of odd order with exactly as many automorphisms as elements, or check the proposed example of order 1009^52359.
| 1 | { |
| 2 | "domain": "mathematics", |
| 3 | "topics": [ |
| 4 | "algebra" |
| 5 | ], |
| 6 | "type": "construction", |
| 7 | "also": [ |
| 8 | "proof" |
| 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": "16.63", |
| 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 | "review": true, |
| 22 | "approval": "first-time" |
| 23 | } |