Question
In each part below, a group G and a subgroup H are given. Determine whether H...
In each part below, a group G and a subgroup H are given. Determine whether H is normal in G. If it is, list the elements of the quotient group G/H. (a) G = Z-15 × Z-20 and H = <(10, 17)> (b) G = S-6 and H = A-6 (c) G = S-5 and H = A-4
Homework Answers
Answer #1
plz do like
Not the answer you're looking for?
Similar Questions
Let H be a normal subgroup of G. Assume the quotient group G/H is abelian. Prove...
Let H be a normal subgroup of G. Assume the quotient group G/H
is abelian. Prove that, for any two elements x, y ∈ G, we have x^
(-1) y ^(-1)xy ∈ H
Let G be a finite group, and suppose that H is normal subgroup of G. Show...
Let G be a finite group, and suppose that H is normal subgroup
of G.
Show that, for every g ∈ G, the order of gH in G/H must divide
the order of g in G.
What is the order of the coset [4]42 +
〈[6]42〉 in Z42/〈[6]42〉?
Find an example to show that the order of gH in G/H does not
always determine the order of g in G. That is, find an example of a
group G, and...
(a) Show that H =<(1234)> is a normal subgroup of G=S4 (b) Is the quotient group...
(a) Show that H =<(1234)> is a normal subgroup of G=S4
(b) Is the quotient group G/H abelian? Justify?
a) Let H be a subgroup of a group G satisfying [G ∶ H] = 2....
a) Let H be a subgroup of a group G satisfying [G ∶ H] = 2. If
there are elements a, b ∈ G such that ab ∈/ H, then prove that
either a ∈ H or b ∈ H. (b) List the left and right cosets of H =
{(1), (23)} in S3. Are they the same collection?
Determine if the indicated subgroup H is a normal subgroup of G. (a) Let G =...
Determine if the indicated subgroup H is a normal subgroup of
G.
(a) Let G = Z and H = 6Z.
(b) Let G = A4 and H =
{id,(12)(34),(13)(24),(14)(23)}.
A subgroup H of a group G is called a normal subgroup if gH=Hg for all...
A subgroup H of a group G is called a normal subgroup if gH=Hg
for all g ∈ G. Every Group contains at least two normal subgroups:
the subgroup consisting of the identity element only {e}; and the
entire group G. If G=S(n) show that A(n) (the subgroup of even
permuations) is also a normal subgroup of G.
For each cyclic group below: (i) List all of the generators for the group. (ii) Determine...
For each cyclic group below: (i) List all of the generators for
the group. (ii) Determine the possible orders of elements of the
group. (iii) Determine the possible orders of subgroups of the
group. (a) <Z-12, +> (b) <Z-15, +> (c) <Z-20, +>
(d) <Z-24, +>
Let G be a finite group and H a subgroup of G. Let a be an...
Let
G be a finite group and H a subgroup of G. Let a be an element of G
and aH = {ah : h is an element of H} be a left coset of H. If B is
an element of G as well show that aH and bH contain the same number
of elements in G.
In each of the following, prove that the specified subset H is not a subgroup of...
In each of the following, prove that the specified subset H is
not a subgroup of the given group G: (a) G = (Z, +), H is the set
of positive and negative odd integers, along with 0. (b) G = (R,
+), H is the set of real numbers whose square is a rational number.
(c) G = (Dn, ◦), H is the set of all reflections in G.
Let G be a group and suppose H = {g5 : g ∈ G} is a...
Let G be a group and suppose H = {g5 : g ∈ G} is a
subgroup of G.
(a) Prove that H is normal subgroup of G.
(b) Prove that every element in G/H has order at most 5.
ADVERTISEMENT
Need Online Homework Help?
Get Answers For Free
Most questions answered within 1 hours.
ADVERTISEMENT
Active Questions
asked 32 minutes ago
asked 37 minutes ago
asked 39 minutes ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago