MTH 421 Exam 1 Question and
answers already passed 2026
multiplication notation - correct answer ✔a^n = a * a * a ...
a^(-n) = a(-1) * a(-1) * a(-1) ....
a^0 = identity element
addition notation - correct answer ✔na = a + a + a ...
(-n)a = (-a) + (-a) + (-a) ...
(0)a = identity element
Abelian group - correct answer ✔n(a+b) = na + nb
(ab) ^ n = a^n b^n
Cyclic Subgroups - correct answer ✔Let (g, *) be a group and a exist in G. Define
<a> = {a^n | n exist in Z} : multiplication
<a> = {na | n exist in Z} : addition
<a> is a subgroup of G
Order of a (ord(a)) - correct answer ✔Let ( G, *) be a group and a in G. The order of a is the least
positive integer n such that a^n = e.
The number of elements in <a>
cyclic - correct answer ✔Let (G, *) be a group. (G, *) is a cyclic if there is some a in G such that <a> = G
answers already passed 2026
multiplication notation - correct answer ✔a^n = a * a * a ...
a^(-n) = a(-1) * a(-1) * a(-1) ....
a^0 = identity element
addition notation - correct answer ✔na = a + a + a ...
(-n)a = (-a) + (-a) + (-a) ...
(0)a = identity element
Abelian group - correct answer ✔n(a+b) = na + nb
(ab) ^ n = a^n b^n
Cyclic Subgroups - correct answer ✔Let (g, *) be a group and a exist in G. Define
<a> = {a^n | n exist in Z} : multiplication
<a> = {na | n exist in Z} : addition
<a> is a subgroup of G
Order of a (ord(a)) - correct answer ✔Let ( G, *) be a group and a in G. The order of a is the least
positive integer n such that a^n = e.
The number of elements in <a>
cyclic - correct answer ✔Let (G, *) be a group. (G, *) is a cyclic if there is some a in G such that <a> = G
