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# Cyclic Groups and Generators

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Let G = <a> be a cyclic group of size 600. What is a generator for the smallest subgroup of G that includes both a^42 and a^70?

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https://brainmass.com/math/group-theory/cyclic-groups-generators-109246

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Since G is a cyclic group of size 600, we can assume that G=<a>, ...

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Cyclic groups and generators are investigated. The response received a rating of "5/5" from the student who originally posted the question.

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## Cyclic Groups, Generators and Orders of Elements

(1) Let G be a group such that
...
Show that G cannot be cyclic.

(2) Show that a cyclic group with one generator has at most 2 elements.

(3) Let a 2 G be an element of order two, and b 2 G an element of order three. Show that HK where H = (a) and K = (b) has order 6.

See the attached file.

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