Packet 7: Bonus 18

Issai Schur generalized this mathematician’s theorem on finite linear groups, which bounds the index of an abelian normal subgroup. For 10 points each:
[10m] What mathematician names a theorem about composition series uniqueness with Otto Hölder? An intuitive but difficult-to-prove theorem named for this man divides the plane into an “interior” and “exterior.”
ANSWER: Camille Jordan [or Marie Ennemond Camille Jordan]
[10e] In linear algebra, Jordan normal form represents an operator using “blocks” whose diagonal elements are these values. These values are the roots of an operator’s characteristic polynomial.
ANSWER: eigenvalues
[10h] The Jordan–Chevalley decomposition of an operator is a sum whose two terms have these two properties. A Lie (“lee”) algebra has one of these two properties if its Jacobson radical is trivial and the other if its derived series vanishes. Name either.
ANSWER: semisimple OR nilpotent [reject “simple”]
<Editors, Other Science> | P. Playoffs 7 (Editors 7)

HeardPPBE %M %H %
1016.00100%60%0%

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Conversion

TeamOpponentPart 1Part 2Part 3TotalParts
BruinJohns Hopkins010010E
CambridgeWashU010010E
Chicago AUC Berkeley A1010020ME
Columbia AIndiana1010020ME
Columbia BRutgers1010020ME
Northwestern AToronto A010010E
Stanford ANYU A1010020ME
TexasUCLA010010E
Toronto BIllinois A1010020ME
UC Berkeley BMaryland A1010020ME

Summary

TournamentEditionMatchHeardPPBE %M %H %
Main Site2026-04-17✓1016.00100%60%0%