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〈a, b | aa=1, ababbb=1〉

Monoid presentation of length 8

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. b8 ⇒ 1
  2. ba ⇒ ab5
  3. a2 ⇒ 1

Cayley table

1ababb2ab2b3ab3b4ab4b5ab5b6ab6b7ab7
11ababb2ab2b3ab3b4ab4b5ab5b6ab6b7ab7
aa1abbab2b2ab3b3ab4b4ab5b5ab6b6ab7b7
bbab5b2ab6b3ab7b4ab5abb6ab2b7ab31ab4
ababb5ab2b6ab3b7ab41ab5bab6b2ab7b3ab4
b2b2ab2b3ab3b4ab4b5ab5b6ab6b7ab71abab
ab2ab2b2ab3b3ab4b4ab5b5ab6b6ab7b7a1abb
b3b3ab7b4ab5abb6ab2b7ab31ab4bab5b2ab6
ab3ab3b7ab41ab5bab6b2ab7b3ab4abb5ab2b6
b4b4ab4b5ab5b6ab6b7ab71ababb2ab2b3ab3
ab4ab4b4ab5b5ab6b6ab7b7a1abbab2b2ab3b3
b5b5abb6ab2b7ab31ab4bab5b2ab6b3ab7b4a
ab5ab5bab6b2ab7b3ab4abb5ab2b6ab3b7ab41
b6b6ab6b7ab71ababb2ab2b3ab3b4ab4b5ab5
ab6ab6b6ab7b7a1abbab2b2ab3b3ab4b4ab5b5
b7b7ab31ab4bab5b2ab6b3ab7b4ab5abb6ab2
ab7ab7b3ab4abb5ab2b6ab3b7ab41ab5bab6b2

Right Cayley graph

Left Cayley graph

Others with same cardinality

26 unique, 135 total

Length:Presentation:Description:Related:
8 〈a, b | bb=aa, abab=1〉 Finite non-Abelian group with 16 elements 4 isomorphic
9 〈a, b | aaaa=b, bbbb=1〉 Isomorphic to ℤ16 67 isomorphic
9 〈a, b | aab=a, bbbb=b〉 Finite non-commutative monoid with 16 elements
10 〈a, b | aaab=ba, abab=1〉 Finite non-Abelian group with 16 elements 7 isomorphic
10 〈a, b | bab=aaa, aabb=1〉 Finite non-Abelian group with 16 elements 6 isomorphic
10 〈a, b | aaaa=a, aabb=b〉 Finite non-commutative monoid with 16 elements 1 isomorphic
10 〈a, b | aaaa=a, bbbb=a〉 Finite commutative monoid with 16 elements 1 isomorphic
10 〈a, b | aaaa=b, bbbb=a〉 Finite commutative monoid with 16 elements 5 isomorphic
10 〈a, b | aba=b, aaaabb=1〉 Finite non-Abelian group with 16 elements 3 isomorphic
10 〈a, b | aba=b, aabbbb=1〉 Finite non-Abelian group with 16 elements 5 isomorphic
11 〈a, b | aaaa=aa, bbbb=a〉 Finite commutative monoid with 16 elements
11 〈a, b | aaaa=ab, bbbb=a〉 Finite commutative monoid with 16 elements 2 isomorphic
11 〈a, b | aaaa=bb, bbbb=a〉 Finite commutative monoid with 16 elements
11 〈a, b | aaab=bb, abba=a〉 Finite non-commutative monoid with 16 elements 2 isomorphic
11 〈a, b | bab=aab, bbb=aa〉 Finite non-commutative monoid with 16 elements
11 〈a, b | bab=aba, bbb=aa〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaaa=a, aabab=b〉 Finite non-commutative monoid with 16 elements 1 isomorphic
11 〈a, b | aab=bb, abbba=a〉 Finite non-commutative monoid with 16 elements 3 isomorphic
11 〈a, b | aaa=ab, babb=bb〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaa=ab, bbaa=bb〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaa=bb, abab=aa〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aba=aa, bbbb=ab〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaa=b, abbbbb=b〉 Finite commutative monoid with 16 elements 2 isomorphic
11 〈a, b | aba=b, aaaa=abb〉 Finite non-commutative monoid with 16 elements
11 〈a, b | ab=aa, bbba=bbb〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aa=a, ababab=bb〉 Finite non-commutative monoid with 16 elements

Other isomorphic instances

40 total

Length:Presentation:
8〈a, b | aa=1, abbbab=1〉
8〈a, b | aa=1, bababb=1〉
8〈a, b | aa=1, babbb=a〉
10〈a, b | aaa=a, ababbb=1〉
10〈a, b | aaa=a, abbbab=1〉
10〈a, b | aaa=a, bababb=1〉
10〈a, b | aab=b, ababbb=1〉
10〈a, b | aab=b, abbbab=1〉
10〈a, b | aab=b, bababb=1〉
10〈a, b | aab=b, babbba=1〉
10〈a, b | aab=b, bbabab=1〉
10〈a, b | aab=b, bbbaba=1〉
10〈a, b | aa=1, aaababbb=1〉
10〈a, b | aa=1, aaabbbab=1〉
10〈a, b | aa=1, aabababb=1〉
10〈a, b | aa=1, aababbba=1〉
10〈a, b | aa=1, aabbabab=1〉
10〈a, b | aa=1, aabbbaba=1〉
10〈a, b | aa=1, abaaabbb=1〉
10〈a, b | aa=1, abaabbab=1〉
10〈a, b | aa=1, ababaabb=1〉
10〈a, b | aa=1, abababba=1〉
10〈a, b | aa=1, ababbaab=1〉
10〈a, b | aa=1, abbaabab=1〉
10〈a, b | aa=1, abbbaaab=1〉
10〈a, b | aa=1, baaababb=1〉
10〈a, b | aa=1, baababab=1〉
10〈a, b | aa=1, babaaabb=1〉
10〈a, b | aa=1, aababbb=a〉
10〈a, b | aa=1, aabbbab=a〉
10〈a, b | aa=1, abababb=a〉
10〈a, b | aa=1, ababbba=a〉
10〈a, b | aa=1, abbabab=a〉
10〈a, b | aa=1, baaabbb=a〉
10〈a, b | aa=1, baabbab=a〉
10〈a, b | aa=1, babaabb=a〉
10〈a, b | aa=1, ababbb=aa〉
10〈a, b | aa=1, abbbab=aa〉
10〈a, b | aa=1, bababb=aa〉
10〈a, b | aa=1, babbb=aaa〉