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Group Theory 13: Cyclic Groups and Order of an element - 3
Автор: S Kumaresan
Загружено: 2025-11-10
Просмотров: 217
Описание:
We prove various results concerning the orders of elements.
(i) If a and b are elements of finite order, then ab may not be of finite order.
(ii) If ab=ba and orders of a and b are relatively prime, then the oder of ab is the product of the orders.
(iii) If ab=ba and the o(a)=m and o(b)=n, then there exists c such that o(c)=lcm(m,n).
(iv) if s=s1.. sr is the cycle decomposition of a permutation s in Sn, then o(s)= lcm(length(s1), .., length(sr)).
This session could be demanding for a beginner, but if you are serious about Algebra, it is worth your time.
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