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〈a, b | aaab=1, bbbbb=1〉

Monoid presentation of length 9

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. a15 ⇒ 1
  2. b ⇒ a12

Cayley table

1aa2a3a4a5a6a7a8a9a10a11a12a13a14
11aa2a3a4a5a6a7a8a9a10a11a12a13a14
aaa2a3a4a5a6a7a8a9a10a11a12a13a141
a2a2a3a4a5a6a7a8a9a10a11a12a13a141a
a3a3a4a5a6a7a8a9a10a11a12a13a141aa2
a4a4a5a6a7a8a9a10a11a12a13a141aa2a3
a5a5a6a7a8a9a10a11a12a13a141aa2a3a4
a6a6a7a8a9a10a11a12a13a141aa2a3a4a5
a7a7a8a9a10a11a12a13a141aa2a3a4a5a6
a8a8a9a10a11a12a13a141aa2a3a4a5a6a7
a9a9a10a11a12a13a141aa2a3a4a5a6a7a8
a10a10a11a12a13a141aa2a3a4a5a6a7a8a9
a11a11a12a13a141aa2a3a4a5a6a7a8a9a10
a12a12a13a141aa2a3a4a5a6a7a8a9a10a11
a13a13a141aa2a3a4a5a6a7a8a9a10a11a12
a14a141aa2a3a4a5a6a7a8a9a10a11a12a13

Right Cayley graph

Others with same cardinality

23 unique, 52 total

Length:Presentation:Description:Related:
9 〈a, b | aaa=bb, aba=a〉 Finite non-commutative monoid with 15 elements 2 isomorphic
9 〈a, b | aaa=bb, aba=b〉 Finite non-commutative monoid with 15 elements 1 isomorphic
9 〈a, b | aaa=a, abbb=b〉 Finite non-commutative monoid with 15 elements 4 isomorphic
10 〈a, b | aaa=bb, aba=aa〉 Finite non-commutative monoid with 15 elements 1 isomorphic
10 〈a, b | aaa=bb, aba=bb〉 Finite non-commutative monoid with 15 elements 2 isomorphic
10 〈a, b | aaa=a, bbbbb=a〉 Finite commutative monoid with 15 elements
10 〈a, b | aaa=b, bbbbb=a〉 Finite commutative monoid with 15 elements
10 〈a, b | aaa=b, bbbbb=b〉 Finite commutative monoid with 15 elements
11 〈a, b | abb=aaa, baaa=b〉 Finite non-commutative monoid with 15 elements 3 isomorphic
11 〈a, b | abb=aaa, baba=b〉 Finite non-commutative monoid with 15 elements 1 isomorphic
11 〈a, b | aab=aaa, aba=bb〉 Finite non-commutative monoid with 15 elements
11 〈a, b | abb=aaa, bbb=ab〉 Finite non-commutative monoid with 15 elements 1 isomorphic
11 〈a, b | abb=aaa, bbb=ba〉 Finite non-commutative monoid with 15 elements
11 〈a, b | aaa=aa, bbbbb=a〉 Finite commutative monoid with 15 elements
11 〈a, b | aaa=ab, baabb=b〉 Finite non-commutative monoid with 15 elements 5 isomorphic
11 〈a, b | aaa=ab, bbbbb=a〉 Finite commutative monoid with 15 elements 1 isomorphic
11 〈a, b | aaa=bb, bbbbb=a〉 Finite commutative monoid with 15 elements 1 isomorphic
11 〈a, b | aaa=ab, bbbb=aa〉 Finite non-commutative monoid with 15 elements
11 〈a, b | aab=aa, bbbb=ab〉 Finite non-commutative monoid with 15 elements
11 〈a, b | aaa=b, bbbbb=ab〉 Finite commutative monoid with 15 elements
11 〈a, b | aab=a, bbbbb=ba〉 Finite non-commutative monoid with 15 elements 1 anti-isomorphic
11 〈a, b | aab=b, bbaa=aaa〉 Finite non-commutative monoid with 15 elements
11 〈a, b | ab=aa, bbaaa=bb〉 Finite non-commutative monoid with 15 elements 6 isomorphic

Other isomorphic instances

138 total

Length:Presentation:
9〈a, b | aaba=1, bbbbb=1〉
9〈a, b | aaa=b, bbbbb=1〉
9〈a, b | aaa=1, abbbbb=1〉
9〈a, b | aaa=1, babbbb=1〉
9〈a, b | aaa=1, bbabbb=1〉
9〈a, b | aaa=1, bbbbb=a〉
10〈a, b | aaaaa=1, aabbb=1〉
10〈a, b | aaaaa=1, ababb=1〉
10〈a, b | aaaaa=1, abbab=1〉
10〈a, b | aaaaa=1, abbba=1〉
10〈a, b | aaaaa=1, baabb=1〉
10〈a, b | aaaaa=1, babab=1〉
10〈a, b | aaaab=1, abbbb=1〉
10〈a, b | aaaab=1, babbb=1〉
10〈a, b | aaaab=1, bbabb=1〉
10〈a, b | aaaab=1, bbbab=1〉
10〈a, b | aaaab=1, bbbba=1〉
10〈a, b | aaaba=1, babbb=1〉
10〈a, b | aaaba=1, bbabb=1〉
10〈a, b | aaaba=1, bbbab=1〉
10〈a, b | aabaa=1, bbabb=1〉
10〈a, b | aaa=bb, bbbbb=1〉
10〈a, b | aaa=1, aabbbbb=1〉
10〈a, b | aaa=1, abbabbb=1〉
10〈a, b | aaa=1, abbbabb=1〉
10〈a, b | aaa=1, abbbbba=1〉
10〈a, b | aaa=1, baabbbb=1〉
10〈a, b | aaa=1, babbabb=1〉
10〈a, b | aaa=1, babbbab=1〉
10〈a, b | aaa=1, bbaabbb=1〉
10〈a, b | aaa=1, bbbbb=aa〉
11〈a, b | aaaa=bbb, abbb=1〉
11〈a, b | aaaa=bbb, babb=1〉
11〈a, b | aaabb=b, bbbbb=1〉
11〈a, b | aabab=b, bbbbb=1〉
11〈a, b | abaab=b, bbbbb=1〉
11〈a, b | ababa=b, bbbbb=1〉
11〈a, b | baaab=b, bbbbb=1〉
11〈a, b | aaab=bb, bbbbb=1〉
11〈a, b | bbb=aaa, aaaaa=1〉
11〈a, b | bbb=aaa, aaaab=1〉
11〈a, b | bbb=aaa, aaaba=1〉
11〈a, b | bbb=aaa, aaabb=1〉
11〈a, b | bbb=aaa, aabaa=1〉
11〈a, b | bbb=aaa, aabab=1〉
11〈a, b | bbb=aaa, aabba=1〉
11〈a, b | bbb=aaa, abaab=1〉
11〈a, b | bbb=aaa, ababa=1〉
11〈a, b | bbb=aaa, abbba=1〉
11〈a, b | aaaaa=1, aaabbb=1〉
11〈a, b | aaaaa=1, aabbba=1〉
11〈a, b | aaaaa=1, baaabb=1〉
11〈a, b | aaaa=a, abbbbb=1〉
11〈a, b | aaaa=a, babbbb=1〉
11〈a, b | aaaa=a, bbabbb=1〉
11〈a, b | aaaa=b, aaabbb=1〉
11〈a, b | aaaa=b, aababb=1〉
11〈a, b | aaaa=b, aabbab=1〉
11〈a, b | aaaa=b, aabbba=1〉
11〈a, b | aaaa=b, abaabb=1〉
11〈a, b | aaaa=b, ababab=1〉
11〈a, b | aaaa=b, ababba=1〉
11〈a, b | aaaa=b, abbaab=1〉
11〈a, b | aaaa=b, baaabb=1〉
11〈a, b | aaaa=b, baabab=1〉
11〈a, b | aaab=b, abbbbb=1〉
11〈a, b | aaab=b, babbbb=1〉
11〈a, b | aaab=b, bbabbb=1〉
11〈a, b | aaab=b, bbbabb=1〉
11〈a, b | aaab=b, bbbbab=1〉
11〈a, b | aaab=b, bbbbba=1〉
11〈a, b | aaba=b, abbbbb=1〉
11〈a, b | aaba=b, babbbb=1〉
11〈a, b | aaba=b, bbabbb=1〉
11〈a, b | aaba=b, bbbabb=1〉
11〈a, b | aaba=b, bbbbab=1〉
11〈a, b | aaba=b, bbbbba=1〉
11〈a, b | aaa=bb, aaabbb=1〉
11〈a, b | aaa=bb, aababb=1〉
11〈a, b | aaa=bb, aabbab=1〉
11〈a, b | aaa=bb, aabbba=1〉
11〈a, b | aaa=bb, abaabb=1〉
11〈a, b | aaa=bb, ababba=1〉
11〈a, b | aaa=bb, abbaab=1〉
11〈a, b | aaa=bb, baaabb=1〉
11〈a, b | aaa=bb, baabab=1〉
11〈a, b | aaab=1, abbbbb=a〉
11〈a, b | aaab=1, babbbb=a〉
11〈a, b | aaab=1, bbabbb=a〉
11〈a, b | aaab=1, bbbabb=a〉
11〈a, b | aaab=1, bbbbab=a〉
11〈a, b | aaab=1, bbbbba=a〉
11〈a, b | aaab=1, bbbbbb=b〉
11〈a, b | aaba=1, abbbbb=a〉
11〈a, b | aaba=1, babbbb=a〉
11〈a, b | aaba=1, bbabbb=a〉
11〈a, b | aaba=1, bbbabb=a〉
11〈a, b | aaba=1, bbbbab=a〉
11〈a, b | aaba=1, bbbbba=a〉
11〈a, b | aaba=1, bbbbbb=b〉
11〈a, b | aaa=b, aaabbbb=1〉
11〈a, b | aaa=b, aababbb=1〉
11〈a, b | aaa=b, aabbabb=1〉
11〈a, b | aaa=b, aabbbab=1〉
11〈a, b | aaa=b, aabbbba=1〉
11〈a, b | aaa=b, abaabbb=1〉
11〈a, b | aaa=b, abababb=1〉
11〈a, b | aaa=b, ababbab=1〉
11〈a, b | aaa=b, ababbba=1〉
11〈a, b | aaa=b, abbaabb=1〉
11〈a, b | aaa=b, abbabab=1〉
11〈a, b | aaa=b, abbabba=1〉
11〈a, b | aaa=b, abbbaab=1〉
11〈a, b | aaa=b, baaabbb=1〉
11〈a, b | aaa=b, baababb=1〉
11〈a, b | aaa=b, baabbab=1〉
11〈a, b | aaa=b, babaabb=1〉
11〈a, b | aaa=b, bababab=1〉
11〈a, b | aaa=b, bbaaabb=1〉
11〈a, b | aaa=1, ababbabb=1〉
11〈a, b | aaa=1, abbababb=1〉
11〈a, b | aaa=1, abbabbab=1〉
11〈a, b | aaa=1, bababbab=1〉
11〈a, b | aaa=1, aabbbbb=a〉
11〈a, b | aaa=1, ababbbb=a〉
11〈a, b | aaa=1, abbabbb=a〉
11〈a, b | aaa=1, abbbabb=a〉
11〈a, b | aaa=1, abbbbab=a〉
11〈a, b | aaa=1, abbbbba=a〉
11〈a, b | aaa=1, bbaabbb=a〉
11〈a, b | aab=1, bbbbbbb=a〉
11〈a, b | aba=1, bbbbbbb=a〉
11〈a, b | aaa=1, abbbbb=aa〉
11〈a, b | aaa=1, bbabbb=aa〉
11〈a, b | aa=b, abbbbbbb=1〉
11〈a, b | aa=b, babbbbbb=1〉
11〈a, b | aa=b, bbabbbbb=1〉
11〈a, b | aa=b, bbbabbbb=1〉