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〈a, b | aaaa=b, bbbb=1〉

Monoid presentation of length 9

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. a16 ⇒ 1
  2. b ⇒ a4

Cayley table

1aa2a3a4a5a6a7a8a9a10a11a12a13a14a15
11aa2a3a4a5a6a7a8a9a10a11a12a13a14a15
aaa2a3a4a5a6a7a8a9a10a11a12a13a14a151
a2a2a3a4a5a6a7a8a9a10a11a12a13a14a151a
a3a3a4a5a6a7a8a9a10a11a12a13a14a151aa2
a4a4a5a6a7a8a9a10a11a12a13a14a151aa2a3
a5a5a6a7a8a9a10a11a12a13a14a151aa2a3a4
a6a6a7a8a9a10a11a12a13a14a151aa2a3a4a5
a7a7a8a9a10a11a12a13a14a151aa2a3a4a5a6
a8a8a9a10a11a12a13a14a151aa2a3a4a5a6a7
a9a9a10a11a12a13a14a151aa2a3a4a5a6a7a8
a10a10a11a12a13a14a151aa2a3a4a5a6a7a8a9
a11a11a12a13a14a151aa2a3a4a5a6a7a8a9a10
a12a12a13a14a151aa2a3a4a5a6a7a8a9a10a11
a13a13a14a151aa2a3a4a5a6a7a8a9a10a11a12
a14a14a151aa2a3a4a5a6a7a8a9a10a11a12a13
a15a151aa2a3a4a5a6a7a8a9a10a11a12a13a14

Right Cayley graph

Others with same cardinality

26 unique, 108 total

Length:Presentation:Description:Related:
8 〈a, b | bb=aa, abab=1〉 Finite non-Abelian group with 16 elements 4 isomorphic
8 〈a, b | aa=1, ababbb=1〉 Finite non-Abelian group with 16 elements 40 isomorphic
9 〈a, b | aab=a, bbbb=b〉 Finite non-commutative monoid with 16 elements
10 〈a, b | aaab=ba, abab=1〉 Finite non-Abelian group with 16 elements 7 isomorphic
10 〈a, b | bab=aaa, aabb=1〉 Finite non-Abelian group with 16 elements 6 isomorphic
10 〈a, b | aaaa=a, aabb=b〉 Finite non-commutative monoid with 16 elements 1 isomorphic
10 〈a, b | aaaa=a, bbbb=a〉 Finite commutative monoid with 16 elements 1 isomorphic
10 〈a, b | aaaa=b, bbbb=a〉 Finite commutative monoid with 16 elements 5 isomorphic
10 〈a, b | aba=b, aaaabb=1〉 Finite non-Abelian group with 16 elements 3 isomorphic
10 〈a, b | aba=b, aabbbb=1〉 Finite non-Abelian group with 16 elements 5 isomorphic
11 〈a, b | aaaa=aa, bbbb=a〉 Finite commutative monoid with 16 elements
11 〈a, b | aaaa=ab, bbbb=a〉 Finite commutative monoid with 16 elements 2 isomorphic
11 〈a, b | aaaa=bb, bbbb=a〉 Finite commutative monoid with 16 elements
11 〈a, b | aaab=bb, abba=a〉 Finite non-commutative monoid with 16 elements 2 isomorphic
11 〈a, b | bab=aab, bbb=aa〉 Finite non-commutative monoid with 16 elements
11 〈a, b | bab=aba, bbb=aa〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaaa=a, aabab=b〉 Finite non-commutative monoid with 16 elements 1 isomorphic
11 〈a, b | aab=bb, abbba=a〉 Finite non-commutative monoid with 16 elements 3 isomorphic
11 〈a, b | aaa=ab, babb=bb〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaa=ab, bbaa=bb〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaa=bb, abab=aa〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aba=aa, bbbb=ab〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aaa=b, abbbbb=b〉 Finite commutative monoid with 16 elements 2 isomorphic
11 〈a, b | aba=b, aaaa=abb〉 Finite non-commutative monoid with 16 elements
11 〈a, b | ab=aa, bbba=bbb〉 Finite non-commutative monoid with 16 elements
11 〈a, b | aa=a, ababab=bb〉 Finite non-commutative monoid with 16 elements

Other isomorphic instances

67 total

Length:Presentation:
9〈a, b | aaaa=1, abbbb=1〉
9〈a, b | aaaa=1, babbb=1〉
9〈a, b | aaaa=1, bbabb=1〉
10〈a, b | aaab=1, bbbbb=a〉
10〈a, b | aaba=1, bbbbb=a〉
10〈a, b | aaa=b, abbbbb=1〉
10〈a, b | aaa=b, babbbb=1〉
10〈a, b | aaa=b, bbabbb=1〉
11〈a, b | aaaa=bbb, bbbb=1〉
11〈a, b | aaaaa=a, abbbb=1〉
11〈a, b | aaaaa=a, babbb=1〉
11〈a, b | aaaaa=a, bbabb=1〉
11〈a, b | aaaab=b, abbbb=1〉
11〈a, b | aaaab=b, babbb=1〉
11〈a, b | aaaab=b, bbabb=1〉
11〈a, b | aaaab=b, bbbab=1〉
11〈a, b | aaaab=b, bbbba=1〉
11〈a, b | aaaba=b, abbbb=1〉
11〈a, b | aaaba=b, babbb=1〉
11〈a, b | aaaba=b, bbabb=1〉
11〈a, b | aaaba=b, bbbab=1〉
11〈a, b | aaaba=b, bbbba=1〉
11〈a, b | aabaa=b, abbbb=1〉
11〈a, b | aabaa=b, babbb=1〉
11〈a, b | aabaa=b, bbabb=1〉
11〈a, b | aaaa=bb, aabbb=1〉
11〈a, b | aaaa=bb, ababb=1〉
11〈a, b | aaaa=bb, abbab=1〉
11〈a, b | aaaa=bb, abbba=1〉
11〈a, b | aaaa=bb, baabb=1〉
11〈a, b | aaaa=bb, babab=1〉
11〈a, b | aaa=bb, aabbbb=1〉
11〈a, b | aaa=bb, abbabb=1〉
11〈a, b | aaa=bb, abbbba=1〉
11〈a, b | aaa=bb, baabbb=1〉
11〈a, b | aaa=bb, babbab=1〉
11〈a, b | aaa=bb, bbaabb=1〉
11〈a, b | aaaa=1, aaabbbb=1〉
11〈a, b | aaaa=1, aabbabb=1〉
11〈a, b | aaaa=1, aabbbba=1〉
11〈a, b | aaaa=1, abababb=1〉
11〈a, b | aaaa=1, ababbab=1〉
11〈a, b | aaaa=1, abbaabb=1〉
11〈a, b | aaaa=1, abbabab=1〉
11〈a, b | aaaa=1, abbabba=1〉
11〈a, b | aaaa=1, baaabbb=1〉
11〈a, b | aaaa=1, baabbab=1〉
11〈a, b | aaaa=1, bababab=1〉
11〈a, b | aaaa=1, bbaaabb=1〉
11〈a, b | aaaa=1, aabbbb=a〉
11〈a, b | aaaa=1, ababbb=a〉
11〈a, b | aaaa=1, abbabb=a〉
11〈a, b | aaaa=1, abbbab=a〉
11〈a, b | aaaa=1, abbbba=a〉
11〈a, b | aaaa=1, babbab=a〉
11〈a, b | aaaa=1, bbaabb=a〉
11〈a, b | aaaa=1, abbbb=aa〉
11〈a, b | aaaa=1, bbabb=aa〉
11〈a, b | aab=1, bbbbbbbb=1〉
11〈a, b | aba=1, bbbbbbbb=1〉
11〈a, b | aa=b, bbbbbbbb=1〉
11〈a, b | aa=1, abbbbbbbb=1〉
11〈a, b | aa=1, babbbbbbb=1〉
11〈a, b | aa=1, bbabbbbbb=1〉
11〈a, b | aa=1, bbbabbbbb=1〉
11〈a, b | aa=1, bbbbabbbb=1〉
11〈a, b | aa=1, bbbbbbbb=a〉