G5096 - Algebra - Cyclic groups 0.0 / 5 ? MathematicsAlgebraCyclic GroupsUniversityNone Created by: callumdavidwattsCreated on: 03-01-17 00:51 526314 Across 1. For a prime p and integer a not divisible by p, then a^(p-1) = 1(mod p) and For a prime p and integer a, then a^p = a(mod p). (7, 6, 7) 4. When an element a∈G whose cyclic subgroup is the group G itself. (6, 5) Down 2. p is prime if an only if (p-1)! = -1(mod p) (7, 7) 3. If x,n∈N are such that (x,n)=1, the x^(ϕ(n)) = 1(mod n) (6, 7) 5. The subgroup generated by an element a∈G of a group G is called the ______ ________ generated by a∈G (6, 8) 6. Let G be a group and a∈G. If there exists a positive integer m such that a^m= 1 where m is the ____ __ __ ______ (if there is no m that makes this true, then it is infinite) (5, 2, 2, 7)
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