Erstellt von William Hartemink
vor mehr als 7 Jahre
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Def: Cyclic Group
Criterion for a^i = a^j
Corollary 1: |a|=|<a>|
Corollary 2: a^k = e implies |a| divides k
Theorem: <a^k> = <a^(gcd(n,k)>
Corollary 1: Oders of Elements in Finite Cyclic Groups
Corollary 2: Criterion for <a^i> = <a^j> and for |a^i| = |a^j|
Corollary 3: Generators of Finite Cyclic Groups
Generators of Z_n
Fundamental Theorem of Cyclic Groups
Corollary Subgroups of Z_n
Def: Phi function
Number of elements of each order in a cyclic group
Corollary: Number of elements of oder d in a finite group