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〈a, b | bb=aa, abab=1〉

Monoid presentation of length 8

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. a8 ⇒ 1
  2. ab ⇒ ba5
  3. b2 ⇒ a2

Cayley table

1aba2baa3ba2a4ba3a5ba4a6ba5a7ba6ba7
11aba2baa3ba2a4ba3a5ba4a6ba5a7ba6ba7
aaa2ba5a3ba6a4ba7a5ba6baa7ba21ba3ba4
bbbaa2ba2a3ba3a4ba4a5ba5a6ba6a7ba71a
a2a2a3ba2a4ba3a5ba4a6ba5a7ba61ba7abba
bababa2a7ba31ba4aba5a2ba6a3ba7a4ba5a6
a3a3a4ba7a5ba6baa7ba21ba3aba4a2ba5ba6
ba2ba2ba3a4ba4a5ba5a6ba6a7ba71babaa2a3
a4a4a5ba4a6ba5a7ba61ba7aba2baa3ba2ba3
ba3ba3ba4aba5a2ba6a3ba7a4ba5baa6ba2a71
a5a5a6baa7ba21ba3aba4a2ba5a3ba6a4ba7b
ba4ba4ba5a6ba6a7ba71babaa2ba2a3ba3a4a5
a6a6a7ba61ba7aba2baa3ba2a4ba3a5ba4ba5
ba5ba5ba6a3ba7a4ba5baa6ba2a7ba31ba4aa2
a7a71ba3aba4a2ba5a3ba6a4ba7a5ba6baba2
ba6ba6ba71babaa2ba2a3ba3a4ba4a5ba5a6a7
ba7ba7ba5baa6ba2a7ba31ba4aba5a2ba6a3a4

Right Cayley graph

Left Cayley graph

Others with same cardinality

26 unique, 171 total

Length:Presentation:Description:Related:
8 〈a, b | aa=1, ababbb=1〉 Finite non-Abelian group with 16 elements 40 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

4 total

Length:Presentation:
10〈a, b | abb=aaa, abab=1〉
10〈a, b | abb=aaa, baba=1〉
10〈a, b | abab=1, aaaba=b〉
10〈a, b | abab=1, abaaa=b〉