Is there a name for the set E(x,n)=\{x^{p}|p \in N

Amiya Arellano

Amiya Arellano

Answered question

2022-02-14

Is there a name for the set E(x,n)={xppNpn1} with xG,G a group?

Answer & Explanation

regresavo552

regresavo552

Beginner2022-02-15Added 14 answers

A common name for E(x,n), considered as a group, is Cn, the cyclic group of order n. So
Cn={e,x,x2,,xn1},
where xn=x0=e.
In the context of your question, Cn=x, where x has order n, e.g., xn=e,but xme for 1m<n.
It is also common to write this by the presentation
Cn=xxn=e.
The "C" stands for "cyclic". Another example of a group presentation is, for the dihedral group Dn,
Dn={r,srn=s2=e,srs=r1},
for n3. This is not a cyclic group in general.

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