(b) Find all bEG with order /b| = 7 bEG. are: (c) Construct in Ga subgroup H with index.(H) = 7

Q: Let G= How many elements does G have?  To what familiar group is G isomorphic?

A:

Q: solve the differential equation y" + 4y = sin^2(x) by i. methods of undetermined coefficient ii.…

A:

Q: Let X,Y be cyclic groups of order 2,3 respectively.  Find the orders of the elements of X×Y.

A: Let X, Y be cyclic groups of order 2,3 respectively then we have to find the   the orders of the…

Q: Show that x is not a generator of the cyclic group (Z3[x]/<x3 +2x + 2>)*. Find one such…

A: Consider the given cyclic group, Z3x/x3+2x+2* It can be observe that x3+2x+2 has no zero in Z3. So,…

Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0, 1, 1).

A:

Q: Prove that the group G = [a, b

A: Given, the group G=a, b with the defining set of relations…

Q: Give an example to show that there exists a group with elements a and b such that la] = 0, \b| = ∞,…

A:

Q: (a) Show that a group G is abelian, if (ab)² = a²b², for a, b € G[C.

A:

Q: If G is a finite group with |G|<160 and G has subgroups of orders 1O, 16 and 20 then the order of G…

A:

Q: If H is a finite subgroup of a group G and x ∈ G, prove that |N(H)| = |N(xHx-1)|.

A: Given: If H is a finite subgroup of a group G and x∈G. To Prove : NH=NxHx-1

Q: Let G be a group and let a e G. In the special case when A = {a}, we write Cg(a) instead of Cg({a})…

A: The given problem is related with group theory. G is a group and a ∈ G. Here, we write Cga instead…

Q: Let G be a finite abelian group

A: Let d = gcd(m; n).We shall use induction on d.Assume  first that d = 1.

Q: (B) Let G be a set of all real numbers except 0. Define on G by a b = |a|b, where lal is the…

A:

Q: Let G = &lt;a, b | a6 = b3 = e, b-1ab = a3&gt;. How many elements doesG have? To what familiar group…

A: Given set is G = &lt;a, b | a^6 = b^3 = e, b^-1ab = a^3&gt;.

Q: If G is a group, prove that Aut(G) and Inn(G) are groups

A:

Q: 9*. Use Lagrange's theorem to prove: If g E G, G a finite group, then gG| = 1.

A: To prove the given statement, assume the following.

Q: Let G be a group, and let H < G. Assume that the number of elements in H is half of the number of…

A:

Q: a) Check whether G = (3n, ·) is a group, where n ∈ Z. b) Let p1 (x) = x3 + 1 and p2 (x) = x4 + x.…

A:

Q: Let G be a group, and let xeG. How are o(x) and o(x) related? Prove your assertion

A: According to the given conditions:

Q: Let G= be a finite cyclic group of order n. Suppose that n = dq where d and q are non-negative…

A:

Q: Let G be a group with IG|=209 then every proper subgroup of G is: * O Non abelian O Non cyclic O…

A: See the detailed solution below.

Q: Show that x is not a generator of the cyclic group (Z3[x]/&lt;x3 + 2x + 2&gt;). Find one such…

A: The given cyclic group is: Z3x/x3+2x+2*. We have to show that x is not the generator of the given…

Q: Suppose x is an element of a cyclic group of order 15 and x3 = x7 = x°. Determine |x13].

A: According to a theorem in group theory , If G is a finite group and a∈G be an element in the group…

Q: (1) Let C₁ = denote the cyclic group of order n. (a) a. Show that C₂ C₁ is a cyclic group. (b) Show…

A: Direct sum of the cyclic group

Q: Let a, b be elements of an abelian group G and let m = |a| and n = |b|. If m and n are relatively…

A:

Q: nite, or Abelian,

A: Given that G is a group, not necessarily cyclic, finite, or Abelian. Let x∈G. The order of the…

Q: Let G be the set (te, ±a, ±b, ±c) where [ 1 10 Show that G form a Group under multiplication.

A: Group: If a set (finite or infinite) together with a binary operation satisfies the four basic…

Q: Let G=.  How many elements does G have?  To what familiar group is G isomorphic?

A: