test_embedding
/mmlu_no_train_abstract_algebra_validation.parquet
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4 columns, 11 rows
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question
(str)
subject
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choices
(list[str])
answer
(i64)
question
subject
The cyclic subgroup of Z_24 generated by 18 has order
abstract_algebra
Find the order of the factor group Z_6/<3>.
abstract_algebra
Statement 1 | A permutation that is a product of m even permutations and n odd permutations is an even permutation if and only if n is even. Statement 2 | Every group is isomorphic to a group of permutations.
abstract_algebra
Find the order of the factor group (Z_4 x Z_12)/(<2> x <2>)
abstract_algebra
Find the maximum possible order for some element of Z_4 x Z_6.
abstract_algebra
Statement 1 | The symmetric group S_3 is cyclic. Statement 2 | Every group is isomorphic to some group of permutations.
abstract_algebra
Statement 1 | If a and b are elements of finite order in an Abelian group, then |ab| is the lcm (|a|,|b|). Statement 2 | If g is a group element and g^n = e, then |g| = n.
abstract_algebra
Statement 1 | If f is a homomorphism from G to K and H is normal in G then f(H) is normal in K. Statement 2 | If f is a homomorphism from G to a group and H is finite subgroup of G, then |f(H)| divides |H|.
abstract_algebra
Find the maximum possible order for an element of S_n for n = 7.
abstract_algebra
Statement 1 | Every integral domain has a field of quotients. Statement 2 | A polynomial of degree n over a ring can have at most n zeros counting multiplicity.
abstract_algebra
Statement 1 | If a group has an element of order 10, then the number of elements of order 10 is divisible by 4. Statement 2 | If m and n are positive integers and phi is the Euler phi function, then phi(mn) = phi(m)phi(n).
abstract_algebra
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