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Science Quiz / Group Theory

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Can you name the answers to these questions?

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Name of theorem stating that the order of any subgroup of a group G is always a proper divisor of the order of G
The regions of a figure unchanged by two conjugate symmetry operations are related by another symmetry of the figure
Normal subgroups must be unions of which partitioning of the group
Only has normal subgroups
One way to define a normal subgroup...
...and another...
...a third way
Group of all permutations of even order
Number of subgroups of a finite group of prime order
ClueAnswer
If g = (12)(345)(67) and k = (174325), find gkg-1
Theorems establishing the existence of subgroups with orders that are prime factors of the order of the group
Groups that are also differential manifolds
Category of group whose only normal subgroups are {e} and the group itself
Type of group with at least one member with the same order as the full group
Dual entity to subgroups; any normal subgroup generates one of these
Credited with originating group theory
Relation f: G->H between two groups (G,*), (H,~) such that f(g1 * g2) = f(g1) ~ f(g2)
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