oddness - 2024 ACF Fall - Buzzpoints App

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 Claremont Colleges	fall	Y	5	20.00	100%	100%	0%
2024 ACF Fall at Cornell	fall	Y	9	15.56	89%	56%	11%
2024 ACF Fall at Illinois	fall	Y	9	18.89	89%	89%	11%
2024 ACF Fall at Rutgers	fall	Y	8	17.50	88%	50%	38%
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	9	17.78	100%	56%	22%
2024 ACF Fall at Georgia	fall	Y	1	10.00	100%	0%	0%
2024 ACF Fall at North Carolina	fall	Y	9	8.89	67%	11%	11%

Data


UCLA E	Claremont B	10	0	10	20
UCLA A	Claremont C	10	0	10	20
Claremont A	UCLA D	10	0	10	20
UCLA C	UCSD	10	0	10	20
USC	UCLA B	10	0	10	20
Cornell E	Binghamton A	10	0	10	20
Binghamton B	Binghamton C	0	0	10	10
Cornell A	Cornell B	0	0	0	0
Cornell C	Cornell D	10	0	10	20
ESF	Cornell F	0	0	10	10
U of Rochester A	Penn State	10	10	10	30
RIT A	Cornell G	10	0	10	20
Syracuse	RIT B	10	0	10	20
U of Rochester B	RIT C	0	0	10	10
Illinois C	Chicago A	10	0	10	20
Purdue C	Illinois D	10	0	10	20
WashU A	Iowa A	10	0	10	20
Notre Dame A	Illinois A	10	0	10	20
Northwestern B	Notre Dame B	10	0	10	20
Notre Dame C	Iowa B	0	0	0	0
Purdue A	SIUE	10	0	10	20
Purdue B	Northwestern A	10	0	10	20
Illinois B	WashU B	10	10	10	30
Columbia J	Columbia B	0	10	10	20
Fordham A	Rutgers A	0	0	10	10
Penn B	Maryland A	10	0	0	10
Penn A	NYU A	10	10	10	30
Maryland B	NYU B	10	0	10	20
Princeton A	Lehigh A	10	10	10	30
Rowan A	Lehigh B	0	0	10	10
Bard A	Rutgers B	0	0	10	10
Jefferson County Scholars	Miami B	0	0	10	10
Michigan A	CWRU C	10	0	10	20
Michigan D	Michigan B	10	0	10	20
Michigan C	West Virginia A	0	0	10	10
Miami C	Michigan State A	0	0	0	0
Ohio State A	West Virginia B	0	0	10	10
Ohio State B	CWRU A	10	0	10	20
Miami A	Ohio State C	0	0	10	10
UW Chastity	Arizona State A	10	0	10	20
UW Wrath	Arizona State B	10	0	10	20
UBC A	UW Gluttony	0	0	10	10
UW Greed	UBC B	0	0	10	10
UW Pride	UW Lust	10	0	10	20
Emory Oxford	Georgia Tech C	0	0	10	10
Georgia Tech E	Auburn C	10	10	10	30
Furman	Clemson A	0	0	10	10
Auburn A	Emory A	0	0	10	10
Georgia Tech B	Georgia A	10	0	10	20
Mississippi State A	Georgia Tech A	10	0	10	20
Georgia Tech D	Southern	0	0	10	10
Tennessee A	South Carolina B	10	10	10	30
South Carolina A	Tennessee B	10	0	10	20
Vanderbilt B	Alabama A	0	0	10	10
Alberta	UW Envy	0	0	10	10
Appalachian State A	Liberty B	0	0	0	0
Liberty C	Appalachian State B	0	0	10	10
UNC A	James Madison A	0	0	10	10
NC State	James Madison B	0	0	0	0
Tusculum	Duke A	10	10	10	30
Virginia	UNC B	0	0	0	0
UNC D	UNC C	0	0	10	10
Virginia Tech A	William & Mary	0	0	10	10
Liberty A	VCU	0	0	10	10