Question
For any prime factor p of the order, some of these objects named after Ludwig Sylow exist. For 10 points each:
[10m] Name these algebraic objects, whose order divides that of their superset according to Lagrange’s Theorem. If their left and right cosets are equal, they are considered “normal.”
ANSWER: subgroups [accept normal subgroups; accept Sylow p-subgroups; do not accept or prompt on groups]
[10h] Normal subgroups are invariant under this operation for elements of the group. This operation divides group elements into “classes” with similar algebraic properties.
ANSWER: conjugation [accept conjugacy classes; accept conjugate elements]
[10e] Normal subgroups are notably closed under this binary set-theoretic operation, which is defined for two sets as the set of elements that lie in both sets at once.
ANSWER: intersection
<Science - Other Science>
Summary
| 2024 Booster Shot (Columbia) | 02/23/2024 | Y | 6 | 3.33 | 33% | 0% | 0% |
| 2024 Booster Shot (Great Lakes) | 03/09/2024 | Y | 6 | 10.00 | 67% | 17% | 17% |
| 2024 Booster Shot (Vanderbilt) | 03/02/2024 | Y | 4 | 7.50 | 75% | 0% | 0% |
| 2024 Booster Shot (WUSTL) | 03/09/2024 | Y | 2 | 10.00 | 100% | 0% | 0% |
| 2024 Booster Shot (Waterloo) | 02/23/2024 | Y | 4 | 20.00 | 75% | 75% | 50% |
Data
| Michigan B | Iowa State | 0 | 0 | 0 | 0 |
| Case Western | Michigan A | 0 | 0 | 0 | 0 |
| Michigan C | WUSTL | 0 | 0 | 10 | 10 |
| North Carolina | Penn State B | 0 | 0 | 10 | 10 |
| Penn State A | Vassar | 10 | 10 | 10 | 30 |
| Stanford | Ohio | 0 | 0 | 10 | 10 |