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Definitions of generator Cyclic Group u0026 Important theorems of cyclic groups | Algebra | SEM-4

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0:00 Introduction
1:00 Definition of Generator.
2:04 Examples on generators.
6:00 Definition of Cyclic Group.
7:35 Examples on cyclic group.
9:42 Every cyclic group is abelian.
12:45 Prove that a group of order 3 must be cyclic.
18:54 Let G be a group and let a ba an element of order n in G, if a power of K is equal to e then n divides k.
22:47 Let G be a cyclic group and a be an element of G let order of G is equal to 24, 'a' power of 8 not equal to e and 'a' power of 12 not equal to e such that order of 'a' is equal to G.
27:46 Find all the groups of z30
31:28 Every group of prime order is cyclic.

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