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〈a, b | baa=abb, abab=1〉

Monoid presentation of length 10

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. ba2 ⇒ ab2
  2. bab ⇒ a3
  3. b3 ⇒ aba
  4. a4 ⇒ 1

Cayley table

1aba2abbab2a3a2babaab2b2aa3ba2baa2b2ab2aa3baa3b2a2b2aa3b2a
11aba2abbab2a3a2babaab2b2aa3ba2baa2b2ab2aa3baa3b2a2b2aa3b2a
aaa2aba3a2babaab21a3ba2baa2b2ab2aba3baa3b2a2b2abab2a3b2ab2a
bbbab2ab2a3b2aabaab2aa2ba1a3ba2b2a2b2aa3b2aa3baaba3b2aa2a2b
a2a2a3a2b1a3ba2baa2b2aba3baa3b2a2b2aabbab2a3b2aabaab2b2aab2a
abababaab2a2b21ab2aa2baa2b2aa3baaba3b2a3b2ab2a2baa2bb2aa3a3b
babaab2a3ab2aa2ba1a3bba2b2aa3b2aa3bab2aba3b2aa2b2aabaa2ba2b2
b2b2b2aabaa3bab2aa2b21a3baa3b2ba2b2aaa2a3b2abaaba3a2bab2a2ba
a3a31a3baba3baa3b2a2abbab2a3b2aa2babaab2b2aa2baa2b2ab2aa2b2a
a2ba2ba2baa2b2a3b2aa2b2aa3baa3b2abaa2abb2b2aab2a3abaa3bab2a1b
abaabaa2b21a2b2aa3baababa3b2ab2a2baab2a2bb2aa3ab2aa2baa3ba3b2
ab2ab2ab2aa2baba2b2aa3b2abab2aba3b2aa2a3b2aabaa2b1a3ba2b2a3ba
b2ab2aa3bab2aa3baa3b2ba2b2ab2a2a3b2abaababaa3a2bab2a2b21a2baa
a3ba3ba3baa3b2b2a2a3b2abab2aabaa3a2bab2ab2aa2b21a2baba2b2aaab
a2baa2baa3b2aa3b2abaa2aba2bb2aab2a3abaa2b2a3bab2a1a2b2aa3babb2
a2b2a2b2a2b2aa3baaba3b2ab2a2abaab2a2bb2aa31ab2aa2baa3baba3b2ba
ab2aab2aba2b2abab2aba3b2aab2a3b2aabaa2ba2ba1a3ba2b2a3b2aa3baa2
a3baa3bab2a2b2aabaa3a2ba3bab2aa2b21a2baa3b2ba2b2aaa3b2abaabab2
a3b2a3b2a3b2abaa2bb2aab2a3a2baa2b2a3bab2a1aa2b2aa3baba2abb2aba
a2b2aa2b2aaba3b2aabaab2a2bb2aa2b21ab2aa2baa3ba3baaba3b2b2a2baa3
a3b2aa3b2aa2bb2aa2baa2b2a3bab2aa3b2aa2b2aa3babbaa2abb2ab2a3aba1

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 | 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 | aab=ba, abbabb=1〉 Finite non-Abelian group with 20 elements 2 isomorphic
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

1 total

Length:Presentation:
10〈a, b | abab=1, abbaa=b〉

Other anti-isomorphic instances

1 total

Length:Presentation:
10〈a, b | abab=1, aabba=b〉