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# ab:aa=b,bb=a a/b aaaa=a b=aa
| 1 | a | a2 | a3 | |
|---|---|---|---|---|
| 1 | 1 | a | a2 | a3 |
| a | a | a2 | a3 | a |
| a2 | a2 | a3 | a | a2 |
| a3 | a3 | a | a2 | a3 |
| Σ | # | Presentation | Description | Related |
|---|---|---|---|---|
| 5 | 7 | ⟨a, b | aa=b, bb=1⟩ | Isomorphic to ℤ4 | 1419 iso |
| 6 | 57 | ⟨a, b | aa=a, bb=a⟩ | Isomorphic to ℕ(4 = 2) | 37 iso |
| 7 | 158 | ⟨a, b | ab=aa, ba=b⟩ | Finite non-commutative monoid with 4 elements | 8 iso, 6 anti-iso |
| 7 | 159 | ⟨a, b | ab=aa, bb=a⟩ | Isomorphic to ℕ(4 = 3) | 16 iso |
| 7 | 242 | ⟨a, b | aa=a, abb=b⟩ | Finite non-commutative monoid with 4 elements | 14 iso |
| 7 | 280 | ⟨a, b | ab=a, bb=aa⟩ | Finite commutative monoid with 4 elements | 17 iso |
| 9 | 2881 | ⟨a, b | aa=a, abbba=b⟩ | Finite commutative monoid with 4 elements | 8 iso |
| 10 | 5033 | ⟨a, b | aaa=aa, abba=b⟩ | Finite commutative monoid with 4 elements | 2 iso |
72 total
| Σ | # | Presentation | Mapping |
|---|---|---|---|
| 7 | 249 | ⟨a, b | aa=b, aab=a⟩ | φ(a) = bb, φ(b) = b |
| 7 | 251 | ⟨a, b | aa=b, aba=a⟩ | φ(a) = bb, φ(b) = b |
| 7 | 260 | ⟨a, b | ab=a, aaa=b⟩ | φ(a) = b, φ(b) = bbb |
| 8 | 900 | ⟨a, b | aa=b, aaaa=a⟩ | φ(a) = bb, φ(b) = b |
| 8 | 923 | ⟨a, b | ab=a, aaab=b⟩ | φ(a) = b, φ(b) = bbb |
| 8 | 925 | ⟨a, b | ab=a, aaba=b⟩ | φ(a) = b, φ(b) = bbb |
| 8 | 929 | ⟨a, b | ab=a, abaa=b⟩ | φ(a) = b, φ(b) = bbb |
| 9 | 2000 | ⟨a, b | aaa=b, aaaa=a⟩ | φ(a) = b, φ(b) = bbb |
| 9 | 2023 | ⟨a, b | aab=a, aaab=b⟩ | φ(a) = bb, φ(b) = b |
| 9 | 2025 | ⟨a, b | aab=a, aaba=b⟩ | φ(a) = bb, φ(b) = b |
| 9 | 2029 | ⟨a, b | aab=a, abaa=b⟩ | φ(a) = bb, φ(b) = b |
| 9 | 2089 | ⟨a, b | aba=a, aaba=b⟩ | φ(a) = bb, φ(b) = b |
| 9 | 2943 | ⟨a, b | ab=a, aaabb=b⟩ | φ(a) = b, φ(b) = bbb |
| 9 | 2947 | ⟨a, b | ab=a, aabab=b⟩ | φ(a) = b, φ(b) = bbb |
| 9 | 2949 | ⟨a, b | ab=a, aabba=b⟩ | φ(a) = b, φ(b) = bbb |
| 9 | 2955 | ⟨a, b | ab=a, abaab=b⟩ | φ(a) = b, φ(b) = bbb |
| 9 | 2957 | ⟨a, b | ab=a, ababa=b⟩ | φ(a) = b, φ(b) = bbb |
| 9 | 2961 | ⟨a, b | ab=a, abbaa=b⟩ | φ(a) = b, φ(b) = bbb |
| 10 | 4650 | ⟨a, b | aaab=a, aaba=b⟩ | φ(a) = b, φ(b) = b |
| 10 | 4654 | ⟨a, b | aaab=a, abaa=b⟩ | φ(a) = b, φ(b) = b |
| 10 | 4660 | ⟨a, b | aaab=a, abbb=b⟩ | φ(a) = b, φ(b) = b |
| 10 | 4701 | ⟨a, b | aaba=a, abaa=b⟩ | φ(a) = b, φ(b) = b |
| 10 | 4732 | ⟨a, b | aabb=a, abab=b⟩ | φ(a) = b, φ(b) = b |
| 10 | 4734 | ⟨a, b | aabb=a, abba=b⟩ | φ(a) = b, φ(b) = b |
| 10 | 4742 | ⟨a, b | abab=a, abba=b⟩ | φ(a) = b, φ(b) = b |
| 10 | 8727 | ⟨a, b | ab=a, aaabbb=b⟩ | φ(a) = b, φ(b) = bbb |
| 10 | 8735 | ⟨a, b | ab=a, aababb=b⟩ | φ(a) = b, φ(b) = bbb |
| 10 | 8739 | ⟨a, b | ab=a, aabbab=b⟩ | φ(a) = b, φ(b) = bbb |
| 10 | 8741 | ⟨a, b | ab=a, aabbba=b⟩ | φ(a) = b, φ(b) = bbb |
| 10 | 8751 | ⟨a, b | ab=a, abaabb=b⟩ | φ(a) = b, φ(b) = bbb |
| 10 | 8755 | ⟨a, b | ab=a, ababab=b⟩ | φ(a) = b, φ(b) = bbb |
| 10 | 8757 | ⟨a, b | ab=a, ababba=b⟩ | φ(a) = b, φ(b) = bbb |
| 10 | 8763 | ⟨a, b | ab=a, abbaab=b⟩ | φ(a) = b, φ(b) = bbb |
| 10 | 8765 | ⟨a, b | ab=a, abbaba=b⟩ | φ(a) = b, φ(b) = bbb |
| 10 | 8769 | ⟨a, b | ab=a, abbbaa=b⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 14330 | ⟨a, b | aaaa=a, aaaaa=b⟩ | φ(a) = bb, φ(b) = b |
| 11 | 14475 | ⟨a, b | aaab=b, aaaab=a⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 14603 | ⟨a, b | aaba=b, aaaab=a⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 14605 | ⟨a, b | aaba=b, aaaba=a⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 14609 | ⟨a, b | aaba=b, aabaa=a⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 14617 | ⟨a, b | aaba=b, abaaa=a⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 14633 | ⟨a, b | aaba=b, baaaa=a⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 18839 | ⟨a, b | aab=a, aaaabb=b⟩ | φ(a) = bb, φ(b) = b |
| 11 | 18843 | ⟨a, b | aab=a, aaabab=b⟩ | φ(a) = bb, φ(b) = b |
| 11 | 18845 | ⟨a, b | aab=a, aaabba=b⟩ | φ(a) = bb, φ(b) = b |
| 11 | 18851 | ⟨a, b | aab=a, aabaab=b⟩ | φ(a) = bb, φ(b) = b |
| 11 | 18853 | ⟨a, b | aab=a, aababa=b⟩ | φ(a) = bb, φ(b) = b |
| 11 | 18857 | ⟨a, b | aab=a, aabbaa=b⟩ | φ(a) = bb, φ(b) = b |
| 11 | 18867 | ⟨a, b | aab=a, abaaab=b⟩ | φ(a) = bb, φ(b) = b |
| 11 | 18869 | ⟨a, b | aab=a, abaaba=b⟩ | φ(a) = bb, φ(b) = b |
| 11 | 18873 | ⟨a, b | aab=a, ababaa=b⟩ | φ(a) = bb, φ(b) = b |
| 11 | 18881 | ⟨a, b | aab=a, abbaaa=b⟩ | φ(a) = bb, φ(b) = b |
| 11 | 18895 | ⟨a, b | aab=a, abbbbb=b⟩ | φ(a) = bb, φ(b) = b |
| 11 | 19101 | ⟨a, b | aba=a, aaabba=b⟩ | φ(a) = bb, φ(b) = b |
| 11 | 19107 | ⟨a, b | aba=a, aababa=b⟩ | φ(a) = bb, φ(b) = b |
| 11 | 19111 | ⟨a, b | aba=a, aabbaa=b⟩ | φ(a) = bb, φ(b) = b |
| 11 | 19121 | ⟨a, b | aba=a, abaaba=b⟩ | φ(a) = bb, φ(b) = b |
| 11 | 24363 | ⟨a, b | ab=a, aaabbbb=b⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 24379 | ⟨a, b | ab=a, aababbb=b⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 24387 | ⟨a, b | ab=a, aabbabb=b⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 24391 | ⟨a, b | ab=a, aabbbab=b⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 24393 | ⟨a, b | ab=a, aabbbba=b⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 24411 | ⟨a, b | ab=a, abaabbb=b⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 24419 | ⟨a, b | ab=a, abababb=b⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 24423 | ⟨a, b | ab=a, ababbab=b⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 24425 | ⟨a, b | ab=a, ababbba=b⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 24435 | ⟨a, b | ab=a, abbaabb=b⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 24439 | ⟨a, b | ab=a, abbabab=b⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 24441 | ⟨a, b | ab=a, abbabba=b⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 24447 | ⟨a, b | ab=a, abbbaab=b⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 24449 | ⟨a, b | ab=a, abbbaba=b⟩ | φ(a) = b, φ(b) = bbb |
| 11 | 24453 | ⟨a, b | ab=a, abbbbaa=b⟩ | φ(a) = b, φ(b) = bbb |