Identities involving the group of functions

Cyclic Identities of rank 2

p=3

General case: (p-1)/2 ∈ Z

Cyclic Identities of rank 3

p=2

p=3

p=4

General case: p ∈ Z

General case: (p-1)/2 ∈ Z

Cyclic Identities of rank 4 and above

r=4, p=2

r=4, p=3

r=5, p=3

Local identities of rank 2

Local identities of rank 3

Rank 3 identities with 3 distinct arguments

Rank 3 identities with 2 distinct arguments

Local identities of rank 4

Rank 4 identities with 4 distinct arguments

Rank 4 identities with 3 distinct arguments

Rank 4 identities with 2 distinct arguments

Higher order local identities

Examples of local identities of rank 5

Local identities of arbitrary rank