question stringclasses 5
values | subject stringclasses 1
value | choices listlengths 4 4 | answer class label 3
classes |
|---|---|---|---|
Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field. | abstract_algebra | [
"0",
"1",
"2",
"3"
] | 1B |
Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G. | abstract_algebra | [
"True, True",
"False, False",
"True, False",
"False, True"
] | 1B |
Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements. | abstract_algebra | [
"True, True",
"False, False",
"True, False",
"False, True"
] | 2C |
Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian. | abstract_algebra | [
"True, True",
"False, False",
"True, False",
"False, True"
] | 0A |
Find the characteristic of the ring 2Z. | abstract_algebra | [
"0",
"3",
"12",
"30"
] | 0A |
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