Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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I need help with 5b
5.
(a) Let G be an abelian group (with the binary operation written as multiplication).
Let N be a fixed positive integer, and let TN = {g € G g = e}. Prove that Ty is a
subgroup of G.
=
(b) Let G be an abelian group. Let T = {g €G: g = e for some positive integer n}.
Prove that T is a subgroup of G. (You don't need this for the proof, but T contains all the
groups TN from (a).)
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Transcribed Image Text:5. (a) Let G be an abelian group (with the binary operation written as multiplication). Let N be a fixed positive integer, and let TN = {g € G g = e}. Prove that Ty is a subgroup of G. = (b) Let G be an abelian group. Let T = {g €G: g = e for some positive integer n}. Prove that T is a subgroup of G. (You don't need this for the proof, but T contains all the groups TN from (a).)
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