Bonus

The Feit–Thompson theorem states that noncyclic groups with this property must have even order or be infinite. For 10 points each:
[10m] Name this property possessed by the 26 sporadic groups. The only normal subgroups of groups with this property are trivial or the entire group.
ANSWER: simple groups [accept finite simple groups]
[10e] Abelian groups that are simple must be cyclic because their binary operation has this property. Matrix multiplication does not have this property.
ANSWER: commutativity [accept commutative]
[10h] A theorem named for this mathematician implies that the order of any finite non-abelian simple group must be divisible by three primes. A free Z-module called this mathematician’s “ring” encodes how a finite group can act on finite sets.
ANSWER: William Burnside [accept Burnside’s theorem or Burnside’s transfer theorem or Burnside’s ring]
<Other Science>
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Conversion

TeamOpponentPart 1Part 2Part 3TotalParts
Arizona StateLSE1010020ME
British ColumbiaPenn State010010E
Chicago AWaterloo A1010020ME
Columbia ARutgers1010020ME
Columbia BUCF010010E
Cornell AMinnesota010010E
Cornell BRIT010010E
FloridaUC Berkeley B1010020ME
Georgia TechHarvard1010020ME
Iowa StateToronto C1010020ME
MITJohns Hopkins010010E
MarylandMichigan1010020ME
NYUYale010010E
Ohio StateIllinois B010010E
OttawaWUSTL B1010020ME
StanfordIndiana1010020ME
TexasVirginia Tech010010E
Toronto ANorth Carolina A010010E
Toronto BChicago B010010E
UC Berkeley ANorthwestern1010020ME
VanderbiltNorth Carolina B010010E
VirginiaWinona State010010E
WUSTL AIllinois A1010020ME
Waterloo BGeorgia State010010E

Summary

TournamentExact Match?HeardPPBEasy %Medium %Hard %
2025 ACF NationalsYes2414.58100%46%0%