| 1 | a | b | a2 | ab | ba | b2 | aba | ab2 | bab | b2a | b3 | (ab)2 | ab2a | (ba)2 | bab2 | b3a | b4 | a(ba)2 | b(ab)2 | bab2a | b4a | (ba)3 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | a | b | a2 | ab | ba | b2 | aba | ab2 | bab | b2a | b3 | (ab)2 | ab2a | (ba)2 | bab2 | b3a | b4 | a(ba)2 | b(ab)2 | bab2a | b4a | (ba)3 |
| a | a | a2 | ab | a | b | aba | ab2 | ba | b2 | (ab)2 | ab2a | (ba)3 | bab | b2a | a(ba)2 | bab2a | b(ab)2 | b4a | (ba)2 | b3a | bab2 | b4 | b3 |
| b | b | ba | b2 | b | bab | b2a | b3 | (ba)2 | bab2 | aba | b3a | b4 | b(ab)2 | bab2a | ab | (ab)2 | b4a | b | (ba)3 | ab2 | a(ba)2 | ba | ab2a |
| a2 | a2 | a | b | a2 | ab | ba | b2 | aba | ab2 | bab | b2a | b3 | (ab)2 | ab2a | (ba)2 | bab2 | b3a | b4 | a(ba)2 | b(ab)2 | bab2a | b4a | (ba)3 |
| ab | ab | aba | ab2 | ab | (ab)2 | ab2a | (ba)3 | a(ba)2 | bab2a | ba | b(ab)2 | b4a | b3a | bab2 | b | bab | b4 | ab | b3 | b2 | (ba)2 | aba | b2a |
| ba | ba | b | bab | ba | b2 | (ba)2 | bab2 | b2a | b3 | b(ab)2 | bab2a | ab2a | aba | b3a | (ba)3 | a(ba)2 | ab2 | ba | ab | b4a | (ab)2 | b | b4 |
| b2 | b2 | b2a | b3 | b2 | aba | b3a | b4 | ab | (ab)2 | (ba)2 | b4a | b | ab2 | a(ba)2 | bab | b(ab)2 | ba | b2 | ab2a | bab2 | (ba)3 | b2a | bab2a |
| aba | aba | ab | (ab)2 | aba | ab2 | a(ba)2 | bab2a | ab2a | (ba)3 | b3a | bab2 | b2a | ba | b(ab)2 | b3 | (ba)2 | b2 | aba | b | b4 | bab | ab | b4a |
| ab2 | ab2 | ab2a | (ba)3 | ab2 | ba | b(ab)2 | b4a | b | bab | a(ba)2 | b4 | ab | b2 | (ba)2 | (ab)2 | b3a | aba | ab2 | b2a | bab2a | b3 | ab2a | bab2 |
| bab | bab | (ba)2 | bab2 | bab | b(ab)2 | bab2a | ab2a | (ba)3 | a(ba)2 | b2a | ab2 | ba | b4a | (ab)2 | b2 | aba | b | bab | b4 | b3 | ab | (ba)2 | b3a |
| b2a | b2a | b2 | aba | b2a | b3 | ab | (ab)2 | b3a | b4 | ab2 | a(ba)2 | bab2a | (ba)2 | b4a | ab2a | (ba)3 | bab2 | b2a | bab | ba | b(ab)2 | b2 | b |
| b3 | b3 | b3a | b4 | b3 | (ba)2 | b4a | b | bab | b(ab)2 | ab | ba | b2 | bab2 | (ba)3 | aba | ab2 | b2a | b3 | bab2a | (ab)2 | ab2a | b3a | a(ba)2 |
| (ab)2 | (ab)2 | a(ba)2 | bab2a | (ab)2 | b3a | bab2 | b2a | b3 | (ba)2 | ab2a | b2 | aba | b4 | bab | ab2 | ba | ab | (ab)2 | b4a | (ba)3 | b | a(ba)2 | b(ab)2 |
| ab2a | ab2a | ab2 | ba | ab2a | (ba)3 | b | bab | b(ab)2 | b4a | b2 | (ba)2 | bab2 | a(ba)2 | b4 | b2a | b3 | bab2a | ab2a | (ab)2 | aba | b3a | ab2 | ab |
| (ba)2 | (ba)2 | bab | b(ab)2 | (ba)2 | bab2 | (ba)3 | a(ba)2 | bab2a | ab2a | b4a | (ab)2 | b3a | b2a | ab2 | b4 | ab | b3 | (ba)2 | b2 | b | aba | bab | ba |
| bab2 | bab2 | bab2a | ab2a | bab2 | b2a | ab2 | ba | b2 | aba | (ba)3 | b | bab | b3 | ab | b(ab)2 | b4a | (ba)2 | bab2 | b3a | a(ba)2 | b4 | bab2a | (ab)2 |
| b3a | b3a | b3 | (ba)2 | b3a | b4 | bab | b(ab)2 | b4a | b | bab2 | (ba)3 | a(ba)2 | ab | ba | bab2a | ab2a | (ab)2 | b3a | aba | b2a | ab2 | b3 | b2 |
| b4 | b4 | b4a | b | b4 | ab | ba | b2 | aba | ab2 | bab | b2a | b3 | (ab)2 | ab2a | (ba)2 | bab2 | b3a | b4 | a(ba)2 | b(ab)2 | bab2a | b4a | (ba)3 |
| a(ba)2 | a(ba)2 | (ab)2 | b3a | a(ba)2 | bab2a | b3 | (ba)2 | bab2 | b2a | b4 | bab | b(ab)2 | ab2a | b2 | b4a | b | (ba)3 | a(ba)2 | ab2 | ab | ba | (ab)2 | aba |
| b(ab)2 | b(ab)2 | (ba)3 | a(ba)2 | b(ab)2 | b4a | (ab)2 | b3a | b4 | ab | bab2a | b3 | (ba)2 | b | aba | bab2 | b2a | bab | b(ab)2 | ba | ab2a | b2 | (ba)3 | ab2 |
| bab2a | bab2a | bab2 | b2a | bab2a | ab2a | b2 | aba | ab2 | ba | b3 | ab | (ab)2 | (ba)3 | b | b3a | b4 | a(ba)2 | bab2a | b(ab)2 | (ba)2 | b4a | bab2 | bab |
| b4a | b4a | b4 | ab | b4a | b | aba | ab2 | ba | b2 | (ab)2 | ab2a | (ba)3 | bab | b2a | a(ba)2 | bab2a | b(ab)2 | b4a | (ba)2 | b3a | bab2 | b4 | b3 |
| (ba)3 | (ba)3 | b(ab)2 | b4a | (ba)3 | a(ba)2 | b4 | ab | (ab)2 | b3a | b | aba | ab2 | bab2a | b3 | ba | b2 | ab2a | (ba)3 | bab2 | bab | b2a | b(ab)2 | (ba)2 |
| Length: | Presentation: | Description: | Related: |
|---|---|---|---|
| 11 | 〈a, b | aba=b, baab=aaa〉 | Finite non-commutative monoid with 23 elements |