Solved Question 1 Let A Be An Element Of A Group And Let Chegg Let a be an element of a group and let ∣a∣=30. compute the orders of the following elements of g. (a) and ∣∣a26∣∣ (b) and ∣∣a17∣∣ (c) and ∣∣a18∣∣. Let g be a group and let a be an element of g with order n. (a) prove (bab 1)n = e. (b) prove that the order of bab 1 is exactly n. by (a), we know that the order of bab 1 is no greater than n. so, suppose that the order of bab 1 is m with m < n. therefore, it must be true that e = (bab 1)m = bamb 1. consequently, b 1eb = b 1bamb 1b.

Solved Question B 1 Let A G G Is Group With The Chegg Let p1; p2; ; pn be distinct positive primes. (p1p2 pn) 1 is divisible by none of these primes. solution: assume that there exists a prime say pi where i n such that pi divides p1p2 pn 1. then clearly pijp1p2 pn and pijp1p2; pn 1 implies that pij1 = (p1 pn 1) (p1 pn): which is impossible as pi 2. hence none of the pi's divides p1 pn 1:. Let g=a8. (do parts b d in a table with columns for the type of element, how many of the type and the order of each type.) a. find the order of g. the order of g is 20,160. b. list all of the types of elements of the group a8 of even permutations using the generic symbols a,b,c,d,e,f,g, and h in standard notation. First, we need to show that the identity element e of g is in h a. since e commutes with all elements of g, we have e a = a e = a. thus, e ∈ h a. 2. next, we need to show that if x, y ∈ h a, then x y ∈ h a. since x, y ∈ h a, we have x a = a x and y a = a y. we want to show that (x y) a = a (x y). using the given equalities, we have:. Let g be a group. an element of g that can be expressed in the form aba^ { 1}b^ { 1} aba−1b−1 for some a, b ∈ g is a commutator in g. the preceding exercise shows that there is a smallest normal subgroup c of a group g containing all commutators in g; the subgroup c is the commutator subgroup of g. show that g c is an abelian group. solution.

Solved 1 Let A Be An Element Of A Group And Let в јaв ј 20 Chegg First, we need to show that the identity element e of g is in h a. since e commutes with all elements of g, we have e a = a e = a. thus, e ∈ h a. 2. next, we need to show that if x, y ∈ h a, then x y ∈ h a. since x, y ∈ h a, we have x a = a x and y a = a y. we want to show that (x y) a = a (x y). using the given equalities, we have:. Let g be a group. an element of g that can be expressed in the form aba^ { 1}b^ { 1} aba−1b−1 for some a, b ∈ g is a commutator in g. the preceding exercise shows that there is a smallest normal subgroup c of a group g containing all commutators in g; the subgroup c is the commutator subgroup of g. show that g c is an abelian group. solution. The order of an element, say g, in a group g is the smallest positive integer n such that g n = e, where e is the identity element of the group. this property helps determine how an element 'repeats' itself within the structure of the group, cyclically returning to the identity element. First, we need to show that the identity element e of g is in h a. since a is an element of g, we have e a = a = a e, so e ∈ h a. 2. next, we need to show that if x y ∈ h a, then x y ∈ h a. if x y ∈ h a, then we have x a = a x and y a = a y. we want to show that x y a = a x y. Compute the orders of the following elements of g. (a) q, a ,a', q12 (b) a, a10 (c) a?, a', aº, a14. here’s the best way to solve it. given | a | = 15, to compute the order of a 3, determine the smallest positive integer k such that (a 3) k = e. question 1. let a be an element of a group and let |al = 15. Let a be an element of a group and let ∣a∣=30. compute the orders of the following elements of g. (a) and ∣∣a26∣∣ (b) and ∣∣a17∣∣ (c) and ∣∣a18∣∣ question #2.

Solved Question A Let G Be A Group And Let H He G Chegg The order of an element, say g, in a group g is the smallest positive integer n such that g n = e, where e is the identity element of the group. this property helps determine how an element 'repeats' itself within the structure of the group, cyclically returning to the identity element. First, we need to show that the identity element e of g is in h a. since a is an element of g, we have e a = a = a e, so e ∈ h a. 2. next, we need to show that if x y ∈ h a, then x y ∈ h a. if x y ∈ h a, then we have x a = a x and y a = a y. we want to show that x y a = a x y. Compute the orders of the following elements of g. (a) q, a ,a', q12 (b) a, a10 (c) a?, a', aº, a14. here’s the best way to solve it. given | a | = 15, to compute the order of a 3, determine the smallest positive integer k such that (a 3) k = e. question 1. let a be an element of a group and let |al = 15. Let a be an element of a group and let ∣a∣=30. compute the orders of the following elements of g. (a) and ∣∣a26∣∣ (b) and ∣∣a17∣∣ (c) and ∣∣a18∣∣ question #2.

Solved Reading Question 7 1 1 Let G Be A Group And Let H Be Chegg Compute the orders of the following elements of g. (a) q, a ,a', q12 (b) a, a10 (c) a?, a', aº, a14. here’s the best way to solve it. given | a | = 15, to compute the order of a 3, determine the smallest positive integer k such that (a 3) k = e. question 1. let a be an element of a group and let |al = 15. Let a be an element of a group and let ∣a∣=30. compute the orders of the following elements of g. (a) and ∣∣a26∣∣ (b) and ∣∣a17∣∣ (c) and ∣∣a18∣∣ question #2.

Solved Let G Be A Group Let A B C Denote Elements Of G Chegg