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MTH 470 Final Quiz All Answers Correct

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MTH 470 Final Quiz All Answers Correct Ring ️a ring R is a set with two binary operations, addition and multiplication, such that for a,b,c in R field ️a commutative division ring division ring (or skew field) of R ️If every nonzero element of R is a unit Left Coset ️aH = {x in G | ...

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  • October 16, 2024
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MTH 470 Final Quiz All Answers Correct

Ring ✔️a ring R is a set with two binary operations, addition and multiplication, such that for a,b,c in R



field ✔️a commutative division ring



division ring (or skew field) of R ✔️If every nonzero element of R is a unit



Left Coset ✔️aH = {x in G | x = ah, for some h in H}



Right Coset ✔️Ha = {x in G | x = ha, for some h in H}



Lagrange Thm ✔️If H is a subgroup of a finite group G, then the order of H divides the order of G



orbit ✔️the set Oa,a = {a^n(a) | n in Z} is the orbit of a under a



every abelian group is cyclic ✔️false



There is at least one abelian group of every finite order > 1 ✔️true



If H and K are subgroups of a group G, then H n K is a group ✔️true



Every cyclic group of order > 3 has at least two generators ✔️true



Every subgroup of a cyclic group is cyclic ✔️true



every cyclic group of order > 2 has at least two distinct generators ✔️true

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