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# ab:aaa=aa,abbba=b ab ab=b ba=b aaa=aa bbb=b
| 1 | a | b | a2 | b2 | |
|---|---|---|---|---|---|
| 1 | 1 | a | b | a2 | b2 |
| a | a | a2 | b | a2 | b2 |
| b | b | b | b2 | b | b |
| a2 | a2 | a2 | b | a2 | b2 |
| b2 | b2 | b2 | b | b2 | b2 |
| Σ | # | Presentation | Description | Related |
|---|---|---|---|---|
| 6 | 44 | ⟨a, b | aa=b, abb=1⟩ | Isomorphic to ℤ5 | 1132 iso |
| 7 | 253 | ⟨a, b | aa=b, abb=a⟩ | Isomorphic to ℕ(5 = 1) | 71 iso |
| 7 | 254 | ⟨a, b | aa=b, abb=b⟩ | Isomorphic to ℕ(5 = 2) | 43 iso |
| 7 | 268 | ⟨a, b | ab=a, baa=b⟩ | Finite non-commutative monoid with 5 elements | 63 iso, 23 anti-iso |
| 8 | 574 | ⟨a, b | aaa=b, aab=b⟩ | Isomorphic to ℕ(5 = 3) | 27 iso |
| 8 | 950 | ⟨a, b | ab=a, bbbb=a⟩ | Isomorphic to ℕ(5 = 4) | 32 iso |
| 8 | 995 | ⟨a, b | ab=a, aaa=bb⟩ | Finite commutative monoid with 5 elements | 19 iso |
| 8 | 1019 | ⟨a, b | ab=a, bba=bb⟩ | Finite non-commutative monoid with 5 elements | 25 iso |
| 8 | 1020 | ⟨a, b | ab=a, bbb=aa⟩ | Finite commutative monoid with 5 elements | 9 iso |
| 8 | 1022 | ⟨a, b | ab=a, bbb=ba⟩ | Finite non-commutative monoid with 5 elements | 4 iso |
| 10 | 8617 | ⟨a, b | aa=a, abbbba=b⟩ | Finite commutative monoid with 5 elements | 3 iso |