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〈a, b | aba=b, aabb=1〉

Monoid presentation of length 8

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. a4 ⇒ 1
  2. ab ⇒ ba3
  3. b2 ⇒ a2

Cayley table

1aba2baa3ba2ba3
11aba2baa3ba2ba3
aaa2ba3a3b1baba2
bbbaa2ba2a3ba31a
a2a2a3ba21ba3abba
bababa2aba3a2ba31
a3a31baaba2a2ba3b
ba2ba2ba31babaa2a3
ba3ba3ba3ba1ba2aa2

Right Cayley graph

Left Cayley graph

Others with same cardinality

44 unique, 1183 total

Length:Presentation:Description:Related:
7 〈a, b | aab=1, bbbb=1〉 Isomorphic to ℤ8 727 isomorphic
7 〈a, b | aa=1, abba=b〉 Finite non-commutative monoid with 8 elements 46 isomorphic
8 〈a, b | aa=a, bbbb=a〉 Finite commutative monoid with 8 elements 48 isomorphic
8 〈a, b | aa=b, bbbb=a〉 Finite commutative monoid with 8 elements 34 isomorphic
8 〈a, b | aa=b, bbbb=b〉 Finite commutative monoid with 8 elements 46 isomorphic
8 〈a, b | aa=a, aba=bb〉 Finite non-commutative monoid with 8 elements 5 isomorphic
8 〈a, b | aa=1, ababa=b〉 Finite non-commutative monoid with 8 elements 13 isomorphic
9 〈a, b | aaa=bb, abb=b〉 Finite commutative monoid with 8 elements 55 isomorphic
9 〈a, b | aaa=bb, bab=a〉 Finite commutative monoid with 8 elements 9 isomorphic
9 〈a, b | aab=aa, baa=b〉 Finite non-commutative monoid with 8 elements 8 isomorphic
9 〈a, b | aab=bb, baa=a〉 Finite non-commutative monoid with 8 elements 4 anti-isomorphic
9 〈a, b | ab=aa, baaa=b〉 Finite non-commutative monoid with 8 elements 6 isomorphic
9 〈a, b | ab=aa, bbbb=a〉 Finite commutative monoid with 8 elements 32 isomorphic
9 〈a, b | bb=aa, aaab=a〉 Finite commutative monoid with 8 elements 3 isomorphic
9 〈a, b | ab=aa, baa=bb〉 Finite non-commutative monoid with 8 elements 1 isomorphic
9 〈a, b | ab=aa, bbb=aa〉 Finite non-commutative monoid with 8 elements 1 isomorphic
9 〈a, b | ab=aa, bbb=ba〉 Finite non-commutative monoid with 8 elements
9 〈a, b | aa=a, abbbb=b〉 Finite non-commutative monoid with 8 elements 14 isomorphic
9 〈a, b | ab=a, baaa=bb〉 Finite non-commutative monoid with 8 elements 9 isomorphic
9 〈a, b | ab=a, bbaa=bb〉 Finite non-commutative monoid with 8 elements 9 isomorphic
10 〈a, b | aab=bb, aaaa=b〉 Finite commutative monoid with 8 elements 18 isomorphic
10 〈a, b | aab=bb, abbb=a〉 Finite commutative monoid with 8 elements 10 isomorphic
10 〈a, b | aba=aa, aaab=b〉 Finite non-commutative monoid with 8 elements 3 isomorphic
10 〈a, b | aab=a, bbaa=bb〉 Finite non-commutative monoid with 8 elements
10 〈a, b | aab=b, aaaa=ba〉 Finite non-commutative monoid with 8 elements
10 〈a, b | aab=b, abaa=aa〉 Finite non-commutative monoid with 8 elements 1 isomorphic
10 〈a, b | aab=b, abbb=aa〉 Finite commutative monoid with 8 elements 4 isomorphic
10 〈a, b | ab=aa, aaaa=bb〉 Finite non-commutative monoid with 8 elements 7 isomorphic
10 〈a, b | ab=a, bbbb=baa〉 Finite non-commutative monoid with 8 elements 2 isomorphic
11 〈a, b | aabb=aa, abaa=b〉 Finite commutative monoid with 8 elements 7 isomorphic
11 〈a, b | aabb=aa, bbba=b〉 Finite non-commutative monoid with 8 elements
11 〈a, b | abbb=aa, bbbb=a〉 Finite commutative monoid with 8 elements 14 isomorphic
11 〈a, b | aab=b, aabaa=aa〉 Finite non-commutative monoid with 8 elements 2 isomorphic
11 〈a, b | aab=a, bbbb=bbb〉 Finite non-commutative monoid with 8 elements
11 〈a, b | aab=b, aaaa=aba〉 Finite non-commutative monoid with 8 elements
11 〈a, b | aab=b, aaaa=abb〉 Finite commutative monoid with 8 elements 1 isomorphic
11 〈a, b | ab=a, aaaaaa=bb〉 Finite commutative monoid with 8 elements
11 〈a, b | ab=a, bbbbbb=aa〉 Finite commutative monoid with 8 elements
11 〈a, b | ab=a, bbbbbb=ba〉 Finite non-commutative monoid with 8 elements
11 〈a, b | ab=a, aaaaa=bbb〉 Finite commutative monoid with 8 elements
11 〈a, b | ab=a, bbbbb=aaa〉 Finite commutative monoid with 8 elements
11 〈a, b | ab=a, bbbbb=bba〉 Finite non-commutative monoid with 8 elements
11 〈a, b | ab=a, bbbb=aaaa〉 Finite commutative monoid with 8 elements
11 〈a, b | ab=a, bbbb=bbba〉 Finite non-commutative monoid with 8 elements

Other isomorphic instances

28 total

Length:Presentation:
8〈a, b | aba=b, abba=1〉
8〈a, b | aba=b, baab=1〉
10〈a, b | aaab=ba, aabb=1〉
10〈a, b | aaab=ba, abba=1〉
10〈a, b | aaab=ba, baab=1〉
10〈a, b | aaab=ba, bbaa=1〉
10〈a, b | aaba=ab, aabb=1〉
10〈a, b | aaba=ab, abba=1〉
10〈a, b | aaba=ab, baab=1〉
10〈a, b | aaba=ab, bbaa=1〉
10〈a, b | abab=aa, abba=1〉
10〈a, b | abab=aa, baab=1〉
10〈a, b | abab=aa, bbaa=1〉
10〈a, b | baba=aa, bbaa=1〉
10〈a, b | aabb=1, aababa=1〉
10〈a, b | aabb=1, abaaab=1〉
10〈a, b | aabb=1, ababaa=1〉
10〈a, b | aabb=1, baaaba=1〉
10〈a, b | aabb=1, babaaa=1〉
10〈a, b | abba=1, aaabab=1〉
10〈a, b | abba=1, aababa=1〉
10〈a, b | abba=1, abaaab=1〉
10〈a, b | abba=1, ababbb=1〉
10〈a, b | abba=1, abbbab=1〉
10〈a, b | abba=1, bababb=1〉
10〈a, b | aba=b, aaabab=1〉
10〈a, b | aba=b, aababa=1〉
10〈a, b | aba=b, abaaab=1〉