
(iii). Assume G is abelian. If ord(a)= 15 and ord(c)= 5, what can ord(ac) equal?
V. More Orders. Let a,b,c be elements of a group G. (i). If ord(a)= 15, what can ord(alº) equal? (ii). If ord(56)= 7, what can ord(6) equal?
Abstract algebra
A. Assume G is an abelian group. Let n > 0 be an integer. Prove that f(x) = ?" is a homomorphism from Got G. B. Assume G is an abelian group. Prove that f(x) = 2-1 is a homomorphism from Got G. C. For the (non-abelian) group S3, is f(x) = --! a homomorphism? Why?
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you answer 4 and 5 please
24. (a) Prove that if G is an abelian group, then (ab) = a*b for any a, b e G. (b) Find an example of a non-abelian group and two elements a and b such that (ab) aºb 5. (a) Prove that if G is a group and a, b e G, then (ab) -1 = b-'a-1 (b) Find an example of a group and two elements a and b such that (ab)...
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only do (c)
= 2m, (b) (5pt) Assume G is a group (may not be abelian) with G me N. Can we find x e G such that o (2) = 2? (c) (5pt) If in problem (b), G is abelian and m is odd, can we find two or more order 2 elements?
a b 5. Let G= { |a E U5, b e Z5}. G is an Abelian group under matrix multiplication (modulo 5). Prove the following: :) a (a) What is G] =? (b) Express G as a direct sum of cyclic groups.
9) A group G is called solvable if there is a sequence of subgroups such that each quotient Gi/Gi-1 is abelian. Here Gi-1 Gi means Gi-1 is a normal subgroup of Gi. For example, any abelian group is solvable: If G s abelian, take Go f1), Gi- G. Then G1/Go G is abelian and hence G is solvable (a) Show that S3 is solvable Suggestion: Let Go- [l),Gı-(123)), and G2 -G. Here (123)) is the subgroup generated by the 3-cycle...
Assume C-50+0.6 (Y -T) G = 15 I = 15 T=2 (a) Y at equilibrium is equal to (b) C at equilibrium is equal to
BRUN CAPUT RRRRRR BBBBB axis ORD cylinder A 5 g bullet is fired at 451.2 m/s into a solid cylinder of mass 27.2 kg and a radius 0.34 m. The cylinder is initially at rest and is mounted on fixed vertical axis that runs through it's center of mass. The line of motion of the bullet is perpendicular to the axle and at a distance 5.4 cm from the center. What is the initial angular momentum of the system? 1.22...
PRACTICE EXAM III 5. A 30-g ice cube is dropped into 160 g of water in a glass. If the water is initially at a temperature of 25 °C and the ice is at 0 °C, what is the final temperature of the drink? ANSWER: 8.5 C
Let traingle ABC have midpoint B' on AC, C' midpoint of AB and G be centroid. If AC=5, AB=5, and CC'=6 find BC.