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〈a, b | aaab=1, bbbbbb=1〉

Monoid presentation of length 10

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. a18 ⇒ 1
  2. b ⇒ a15

Cayley table

1aa2a3a4a5a6a7a8a9a10a11a12a13a14a15a16a17
11aa2a3a4a5a6a7a8a9a10a11a12a13a14a15a16a17
aaa2a3a4a5a6a7a8a9a10a11a12a13a14a15a16a171
a2a2a3a4a5a6a7a8a9a10a11a12a13a14a15a16a171a
a3a3a4a5a6a7a8a9a10a11a12a13a14a15a16a171aa2
a4a4a5a6a7a8a9a10a11a12a13a14a15a16a171aa2a3
a5a5a6a7a8a9a10a11a12a13a14a15a16a171aa2a3a4
a6a6a7a8a9a10a11a12a13a14a15a16a171aa2a3a4a5
a7a7a8a9a10a11a12a13a14a15a16a171aa2a3a4a5a6
a8a8a9a10a11a12a13a14a15a16a171aa2a3a4a5a6a7
a9a9a10a11a12a13a14a15a16a171aa2a3a4a5a6a7a8
a10a10a11a12a13a14a15a16a171aa2a3a4a5a6a7a8a9
a11a11a12a13a14a15a16a171aa2a3a4a5a6a7a8a9a10
a12a12a13a14a15a16a171aa2a3a4a5a6a7a8a9a10a11
a13a13a14a15a16a171aa2a3a4a5a6a7a8a9a10a11a12
a14a14a15a16a171aa2a3a4a5a6a7a8a9a10a11a12a13
a15a15a16a171aa2a3a4a5a6a7a8a9a10a11a12a13a14
a16a16a171aa2a3a4a5a6a7a8a9a10a11a12a13a14a15
a17a171aa2a3a4a5a6a7a8a9a10a11a12a13a14a15a16

Right Cayley graph

Others with same cardinality

18 unique, 71 total

Length:Presentation:Description:Related:
8 〈a, b | aa=1, abbba=b〉 Finite non-commutative monoid with 18 elements 14 isomorphic
9 〈a, b | aa=1, abbbbb=b〉 Finite non-commutative monoid with 18 elements 22 isomorphic, 9 anti-isomorphic
10 〈a, b | aba=a, aaab=bb〉 Finite non-commutative monoid with 18 elements
10 〈a, b | aba=b, baab=aa〉 Finite non-commutative monoid with 18 elements
10 〈a, b | aba=b, bbbb=aa〉 Finite non-commutative monoid with 18 elements
10 〈a, b | bb=aa, aaaba=b〉 Finite non-commutative monoid with 18 elements 2 isomorphic
10 〈a, b | aa=a, bbbbb=ab〉 Finite non-commutative monoid with 18 elements 1 isomorphic
10 〈a, b | aa=1, abababa=b〉 Finite non-commutative monoid with 18 elements 2 isomorphic
11 〈a, b | aaaa=ab, babb=b〉 Finite non-commutative monoid with 18 elements 2 isomorphic
11 〈a, b | aab=bb, bbbba=a〉 Finite non-commutative monoid with 18 elements
11 〈a, b | aaa=ab, bbbb=ab〉 Finite non-commutative monoid with 18 elements
11 〈a, b | aaa=ab, bbbb=ba〉 Finite non-commutative monoid with 18 elements
11 〈a, b | aab=bb, baba=aa〉 Finite non-commutative monoid with 18 elements
11 〈a, b | aaa=a, bbbbbb=a〉 Finite commutative monoid with 18 elements
11 〈a, b | aaa=b, bbbbbb=a〉 Finite commutative monoid with 18 elements
11 〈a, b | aaa=b, bbbbbb=b〉 Finite commutative monoid with 18 elements
11 〈a, b | aab=b, bbbba=aa〉 Finite non-commutative monoid with 18 elements
11 〈a, b | bb=aa, ababa=aa〉 Finite non-commutative monoid with 18 elements 1 isomorphic

Other isomorphic instances

33 total

Length:Presentation:
10〈a, b | aaba=1, bbbbbb=1〉
10〈a, b | aaa=b, bbbbbb=1〉
10〈a, b | aaa=1, abbbbbb=1〉
10〈a, b | aaa=1, babbbbb=1〉
10〈a, b | aaa=1, bbabbbb=1〉
10〈a, b | aaa=1, bbbabbb=1〉
10〈a, b | aaa=1, bbbbbb=a〉
11〈a, b | aaaa=bb, abbbb=1〉
11〈a, b | aaaa=bb, babbb=1〉
11〈a, b | aaaa=bb, bbabb=1〉
11〈a, b | aabab=1, bbbbbb=1〉
11〈a, b | abaab=1, bbbbbb=1〉
11〈a, b | ababa=1, bbbbbb=1〉
11〈a, b | aaaa=b, aabbbb=1〉
11〈a, b | aaaa=b, ababbb=1〉
11〈a, b | aaaa=b, abbabb=1〉
11〈a, b | aaaa=b, abbbab=1〉
11〈a, b | aaaa=b, abbbba=1〉
11〈a, b | aaaa=b, baabbb=1〉
11〈a, b | aaaa=b, bababb=1〉
11〈a, b | aaaa=b, babbab=1〉
11〈a, b | aaaa=b, bbaabb=1〉
11〈a, b | aaa=1, aabbbbbb=1〉
11〈a, b | aaa=1, abbabbbb=1〉
11〈a, b | aaa=1, abbbbabb=1〉
11〈a, b | aaa=1, abbbbbba=1〉
11〈a, b | aaa=1, baabbbbb=1〉
11〈a, b | aaa=1, babbabbb=1〉
11〈a, b | aaa=1, babbbbab=1〉
11〈a, b | aaa=1, bbaabbbb=1〉
11〈a, b | aaa=1, bbabbabb=1〉
11〈a, b | aaa=1, bbbaabbb=1〉
11〈a, b | aaa=1, bbbbbb=aa〉