Show that every permutational product of a finite amalgam am(A,B: H) is finite.Hence show that every...

Show that every permutational product of a finite amalgam am(A,B: H) is finite.Hence show that every finite amalgam of two groups is embeddable in a finite group.

Expert Solution

Colby Messinger answered 2 months ago

show that if H is a p sylow subgroup of a finite group G then for...

show that if H is a p sylow subgroup of a finite group G then for an arbitrary x in G x^-1 H x is also a p sylow subgroup of G

Incorrect Theorem. Let H be a finite set of n horses. Suppose that, for every subset...

Incorrect Theorem. Let H be a finite set of n horses. Suppose that, for every subset S ⊂ H with |S| < n, the horses in S are all the same color. Then every horse in H is the same color. i) Prove the theorem assuming n ≥ 3. ii) Why aren’t all horses the same color? That is, why doesn’t your proof work for n = 2?

Show that if a and b are integers with a ≡ b (mod p) for every...

Show that if a and b are integers with a ≡ b (mod p) for every prime p, then it must be that a = b

Using Kurosch's subgroup theorem for free proucts,prove that every finite subgroup of the free product of...

Using Kurosch's subgroup theorem for free proucts,prove that every finite subgroup of the free product of finite groups is isomorphic to a subgroup of some free factor.

Suppose {a1,...,am} is a complete set of representatives for Z/mZ. Show: (i) If (b,m)=1, then{ba1,...,bam}is a...

Suppose {a1,...,am} is a complete set of representatives for Z/mZ. Show: (i) If (b,m)=1, then{b*a1,...,b*am}is a complete set of representatives. (ii) If (b,m)> 1, then{b*a1,...,b*am}is not a complete set of representatives.

Hello! I am stuck on the following question: Show that every simple subgroup of S_4 is...

Hello! I am stuck on the following question: Show that every simple subgroup of S_4 is abelian.

Let B be a finite commutative group without an element of order 2. Show the mapping...

Let B be a finite commutative group without an element of order 2. Show the mapping of b to b2 is an automorphism of B. However, if |B| = infinity, does it still need to be an automorphism?

Let B be a basis of Rn, and suppose that Mv=λv for every v∈B. a) Show...

Let B be a basis of Rn, and suppose that Mv=λv for every v∈B. a) Show that every vector in Rn is an eigenvector for M. b) Hence show that M is a diagonal matrix with respect to any other basis C for Rn.

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 and the intersection of aH bH is non-empty then aH and bH contain the same number of elements in G. Thus conclude that the number of elements in H, o(H), divides the number of elements...

Prove that every nontrivial finite group has a composition series

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