Cyclic Group

The cyclic group $C_n$ with $n$ elements is the simplest kind of group. It's a commutative group which consists of all rotations of a regular $n$-gon, or all integers mod $n$ under addition, or all primitive $n$th roots of unity under multiplication, or other equivalent isomorphic realizations (as groups). In terms of permutations of a ciphertext alphabet of $n$ letters, isomorphic ciphers using this as the underlying group have alphabets consisting of all the cyclic rotations of the alphabet. These are exactly the (classical) ciphertext-autokey (CTAK) ciphers, and they are chainable without conflicts (assuming no plaintext typos).