AMC 8 College Mathematics

Cyclic Groups in TIFR Entrance

Concept – Cyclic Groups

Let’s discuss the concept of Cyclic Groups.

A cyclic group G is a group that can be generated by a single element. In particular, if $ G = \{ a, b, c, d, .. \} $, $ * $ is the group operation and $ a $ is a generating element, then if we compute $a $ , $a*a$, , $a*a*a $, etc. we will be able to create all members of the set G.

Get motivated – Problem from TIFR Entrance

Suppose G is a cyclic group with 60 elements. How many generators are there?

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