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]
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Summary

2024 ACF Fall at CornellfallY915.5689%56%11%
2024 ACF Fall at Ohio StatefallY812.5088%38%0%
2024 ACF Fall at WashingtonfallY615.00100%50%0%
2024 ACF Fall at GeorgiafallY1119.09100%64%27%
2024 ACF Fall at North CarolinafallY98.8967%11%11%
2024 ACF Fall at Claremont CollegesfallY520.00100%100%0%
2024 ACF Fall at RutgersfallY817.5088%50%38%
2024 ACF Fall at IllinoisfallY918.8989%89%11%

Data

Cornell EBinghamton A1001020
Binghamton BBinghamton C001010
Cornell ACornell B0000
Cornell CCornell D1001020
ESFCornell F001010
U of Rochester APenn State10101030
RIT ACornell G1001020
SyracuseRIT B1001020
U of Rochester BRIT C001010