Let a be the generator of a cyclic group G such that o (a) = n . Then For m ∈ Z , am = e  m ≡ 0 (mod n ) In general , ar = as  r ≡ s (modn ) for r , s ∈ Z .

Let a be the generator of a cyclic group G such that o (a) = n . Then For m ∈ Z , am = e  m ≡ 0 (mod n ) In general , ar = as  r ≡ s (modn ) for r , s ∈ Z .

January 19, 2020

B.Sc II [ Semester IV (Paper - VII )

Unit - 1 [Some special groups ]

Order of a generator of a cyclic group :-

Let a be the generator of a cyclic group G such that o (a) = n . Then For m ∈ Z , am = e  m ≡ 0 (mod n ) In general , ar = as  r ≡ s (modn ) for r , s ∈ Z .

Let a be the generator of a cyclic group G such that o (a) = n . Then For m ∈ Z , am = e  m ≡ 0 (mod n ) In general , ar = as  r ≡ s (modn ) for r , s ∈ Z .

Let a be the generator of a cyclic group G such that o (a) = n . Then For m ∈ Z , am = e  m ≡ 0 (mod n ) In general , ar = as  r ≡ s (modn ) for r , s ∈ Z .

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