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〈a, b | aab=ba, abbabb=1〉

Monoid presentation of length 11

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. a5 ⇒ 1
  2. ab ⇒ ba3
  3. b4 ⇒ 1

Cayley table

1aba2bab2a3ba2b2ab3a4ba3b2a2b3aba4b2a3b3a2b2a4b3a3b3a4
11aba2bab2a3ba2b2ab3a4ba3b2a2b3aba4b2a3b3a2b2a4b3a3b3a4
aaa2ba3a3ba4b2a4a4bb2b3a21bab2ab3a3ba2b2a2b3a4b2a3b3b3a
bbbab2ba2b2ab3ba3b2a2b3a1ba4b2a3b3a2ab2a4b3a3a2b3a4a3a4
a2a2a3baa4ba2b2a31ba3b2a4b3a4aba4b2b3bb2ab3ab2a2b3a2b3a3
bababa2b2a3ba3b2a4b3a4ba4b2b3a2bb2ab3aa3b2a2b3a2a4b3a31a
b2b2b2ab3b2a2b3a1b2a3b3a2abb2a4b3a3a2bab3a4a3ba2a4ba3ba4
a3a3a4ba41bb2a2abab2a3b3aa2ba2b2a4b3a2ba3b2b3a3b2ab3a4b3
ba2ba2ba3b2aba4b2a2b3a3bb2a3b3a4a4bab2a4b31b2b3aab3a2a2a3
b2ab2ab2a2b3a3b2a3b3a4a4b2a4b31ba2b2b3aaba3b3a2a2ba4a3bba
b3b3b3a1b3a2abb3a3a2bab2b3a4a3ba2b2aa4ba3b2a2ba4b2a3b2a4
a4a41ba2aba3b2aa2ba4b2a2b3a3a3bb2a3b3a4bab2a4b3b2b3ab3a2
ba3ba3ba4b2a4bb2b3a2bab2ab3a3aba2b2a2b3a4a2b2a3b3a3b3aa41
b2a2b2a2b2a3b3ab2a4b3a2a3b2b3a3a4ba4b2ab3a41bb3abaa2ba2ba3
b3ab3ab3a2a3b3a3a4ba4b3a41bb2a2b3abab2a3a2ba2b2a4ba3b2b2a
ba4ba4bb2a2bab2a3b3aba2b2a4b3a2a3ba3b2b3a3a4b2ab3a41b3aa2
b2a3b2a3b2a4b3a4b2b3a2b2ab3aa3bab2a2b3a2a4ba2b3a31ba3aba4b
b3a2b3a2b3a3ab3a4a2ba3b3a3ba4b2a4b3aa4bb21bab2aba2b2a2b2a3
b2a4b2a4b2b3a2b2ab3a3ab2a2b3a4a2ba3b2a3b3a3ba4b3aa4b1baba2
b3a3b3a3b3a4a4b31ba2b3aaba3b2ab3a2a2ba4b2a2a3bb2a3bab2a4b2
b3a4b3a4b3a2b3aa3bab3a2a4ba2b2a3b3a31ba3b2a4aba4b2bb2ab2a2

Right Cayley graph

Left Cayley graph

Others with same cardinality

28 unique, 63 total

Length:Presentation:Description:Related:
8 〈a, b | aab=a, bbbb=1〉 Finite non-commutative monoid with 20 elements 3 isomorphic, 1 anti-isomorphic
8 〈a, b | ab=aa, bbbb=1〉 Finite non-commutative monoid with 20 elements 1 isomorphic
9 〈a, b | abab=a, bbbb=1〉 Finite non-commutative monoid with 20 elements 2 isomorphic
9 〈a, b | aba=ab, bbbb=1〉 Finite non-commutative monoid with 20 elements 1 isomorphic, 1 anti-isomorphic
9 〈a, b | ab=aa, bbbb=b〉 Finite non-commutative monoid with 20 elements
10 〈a, b | abb=aab, aaaa=1〉 Finite non-commutative monoid with 20 elements 2 isomorphic
10 〈a, b | baa=abb, abab=1〉 Finite non-Abelian group with 20 elements 1 isomorphic, 1 anti-isomorphic
10 〈a, b | aaaaa=1, abbbb=1〉 Isomorphic to ℤ20 16 isomorphic
10 〈a, b | aab=bb, aaaa=a〉 Finite non-commutative monoid with 20 elements
10 〈a, b | aaa=bb, bab=aa〉 Finite non-commutative monoid with 20 elements 1 isomorphic
10 〈a, b | aba=a, aaaa=bb〉 Finite non-commutative monoid with 20 elements
10 〈a, b | aba=b, aaaa=bb〉 Finite non-commutative monoid with 20 elements
10 〈a, b | ab=aa, bbbb=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aaaa=aa, abbb=b〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aaab=bb, bbba=a〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aaaa=a, bbbbb=a〉 Finite commutative monoid with 20 elements
11 〈a, b | aaaa=b, bbbbb=a〉 Finite commutative monoid with 20 elements
11 〈a, b | aaaa=b, bbbbb=b〉 Finite commutative monoid with 20 elements
11 〈a, b | aba=bb, baaab=a〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aab=aa, baba=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aba=aa, aaaa=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aba=aa, aaab=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aba=bb, abb=aaa〉 Finite non-commutative monoid with 20 elements
11 〈a, b | aaaa=1, aaabab=b〉 Finite non-commutative monoid with 20 elements 1 isomorphic
11 〈a, b | aaaa=1, aabab=ab〉 Finite non-commutative monoid with 20 elements 1 isomorphic
11 〈a, b | aba=b, aaaaabb=1〉 Finite non-Abelian group with 20 elements 3 isomorphic
11 〈a, b | aab=a, bbbbb=bb〉 Finite non-commutative monoid with 20 elements
11 〈a, b | ab=aa, bbbb=bbb〉 Finite non-commutative monoid with 20 elements

Other isomorphic instances

2 total

Length:Presentation:
11〈a, b | aab=ba, babbab=1〉
11〈a, b | aab=ba, bbabba=1〉