Question
Feit and Thompson showed every finite group whose order has this property is solvable. For 10 points each:
[10m] Name this property possessed by permutations whose sign is negative. Functions with this property satisfy [read slowly] f of minus x equals minus f of x.
ANSWER: oddness
[10h] A group is solvable if it has a sequence described by the sub-form of this property whose quotients are abelian. Quotient groups are well defined for subgroups described by this word, which are invariant under conjugation.
ANSWER: normal subgroups [accept subnormal sequence]
[10e] All subgroups are normal for abelian groups, whose binary operations have this property. Matrix multiplication lacks this property, which a binary operation has if a times b always equals b times a.
ANSWER: commutativity [or commutative]
<Other Science>
Summary
| 2024 ACF Fall at Cornell | fall | Y | 9 | 15.56 | 89% | 56% | 11% |
| 2024 ACF Fall at Ohio State | fall | Y | 8 | 12.50 | 88% | 38% | 0% |
| 2024 ACF Fall at Washington | fall | Y | 6 | 15.00 | 100% | 50% | 0% |
| 2024 ACF Fall at Georgia | fall | Y | 11 | 19.09 | 100% | 64% | 27% |
| 2024 ACF Fall at North Carolina | fall | Y | 9 | 8.89 | 67% | 11% | 11% |
| 2024 ACF Fall at Claremont Colleges | fall | Y | 5 | 20.00 | 100% | 100% | 0% |
| 2024 ACF Fall at Rutgers | fall | Y | 8 | 17.50 | 88% | 50% | 38% |
| 2024 ACF Fall at Illinois | fall | Y | 9 | 18.89 | 89% | 89% | 11% |
Data
| Jefferson County Scholars (DII) | Miami B (UG) | 0 | 0 | 10 | 10 |
| Michigan A (UG) | CWRU C (UG) | 10 | 0 | 10 | 20 |
| Michigan D (UG) | Michigan B (UG) | 10 | 0 | 10 | 20 |
| Michigan C | West Virginia A (UG) | 0 | 0 | 10 | 10 |
| Miami C (DII) | Michigan State A | 0 | 0 | 0 | 0 |
| Ohio State A (UG) | West Virginia B (UG) | 0 | 0 | 10 | 10 |
| Ohio State B (DII) | CWRU A (UG) | 10 | 0 | 10 | 20 |
| Miami A (UG) | Ohio State C (DII) | 0 | 0 | 10 | 10 |