If G is a finite group with IG|<120 and G has subgroups of orders 10, 15 and 20 then the order of G is: 80 30 O 90 O 60

Q: Prove the next statement: If G is an abelian group of finite order n, then G has a subgroup of…

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Q: Let G be a finite cyclic group and a be an element of G of order 8 then the order of G would be: O…

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Q: Let f be the following permutation: 1 2 3 4 5 6 7 f = 4 3 6 2 1 5 7 a. Determine the group to which…

A: Given permutation is f=12345674362157 f is permutation of 7 elements so it is belong to s7. i.e. sn…

Q: Let G be a finite group of order n . Let g be an element of G with order k. Prove that k|n

A: To prove ''Let G be a finite group of order n . Let g be an element of G with order k. Prove that…

Q: 1. Let p be a prime. A group G (either finite or infinite) is called p-group if the order of every…

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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…

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Q: Let K be a group with 8 elements. Let H be a subgroup of K and H<K. It is known that the order of H…

A: Given:- K is a group with 8 elements , H is a subgroup of K and H&lt;K. H has order of atleast 3.…

Q: If G = {1, 2, 3, 4, 5, 6} is the upper group of multiplication modulo 7, H is a subgroup of G with H…

A: Given: Group G=1,2,3,4,5,6 under multiplication modulo 7. Subgroup H=1,2,4 of G. To find:   a) Right…

Q: @1: Let G be a finite group and aEG 1.t la1= 12. If H= <a) find all other generalrs of H.

A: Let G be a finite group and a∈G such that a=12. If H=a, find all other generators of H. H is a…

Q: Let N be a normal subgroup of a finite group G.  Prove that the order of the group element gN in G/N…

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Q: Suppose that A is subset of a group G such that              A = {a : a2 =e  , a in G }    Where e…

A: Sol:- The subset A consists of all elements a in the group G such that a squared is equal to the…

Q: O O O O If G is a finit subgroups c order of G is 80 60 90- 30

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Q: Let G be a group and a e G. Show that o(a) = o(a-). order n, then ba also has order n.

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Q: If H is the only subgroup of order o(H) in  a finite group G, show that H is the normal  subgrop of…

A: is the only subgroup of order in a finite group .We have to show that  is a normal subgroup of

Q: Let K and H be subgroups of a finite group G with KCHCG. If [G:H] = 4 and [H:K] = 3. Then, [G:K] =…

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Q: 4. Let G be a finite group of order 4 containing no element of order 4. Explain why every…

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Q: Let K and H be subgroups of a finite group G with KCHCG.If[G:H] = 4 and [H:K] = 3. Then, [G:K] = 3 4…

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Q: If G is a finite group with |G|<180 and G has subgroups of orders 10, 18 ano then the order of G is:…

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Q: 3. Let G be a finite group of order n and identity element 1. a. Show that g" = 1 for any g€ G. b.…

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Q: If G = {1, 2, 3, 4, 5, 6} is the upper group of multiplication modulo 7, H is a subgroup of G with H…

A: Given G = {1, 2, 3, 4, 5, 6} is the upper group of multiplication modulo 7, H is a subgroup of G…

Q: Let G be a finite group and p be an odd prime number. Show that G can not have exactly p elements of…

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Q: et G be a group and suppose that x E G has order n. Let d be a divisor of n. Show that G as an…

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Q: 1)Let G be a group and H be a subgroup of G then, for any a, b e G,a = b mod H + (a + b-1) H = H.…

A: Given: To show the correct option is true or false as follows,

Q: Let G Są and let K = {1,(1 2)(3 4), (1 3)(2 4), (1 4)(2 3)}. K is a normal subgroup of G. What is…

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