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〈a, b | aba=b, aabbbb=1〉

Monoid presentation of length 10

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. a4 ⇒ 1
  2. ab ⇒ ba3
  3. b4 ⇒ a2

Cayley table

1aba2bab2a3ba2b2ab3ba3b2a2b3ab2a3b3a2b3a3
11aba2bab2a3ba2b2ab3ba3b2a2b3ab2a3b3a2b3a3
aaa2ba3a3bb2a1bab2a2b3a3ba2b2a3b3b2b3ab3a2
bbbab2ba2b2ab3ba3b2a2b3aa2b2a3b3a2a3b3a31a
a2a2a3ba21ba3b2a2abb2a3b3a2bab2b3a3b2ab3b3a
bababa2b2a3ba3b2b3abb2ab3a2ab2a2b3a3a2b3a31
b2b2b2ab3b2a2b3aa2b2a3b3a2a3ba2b3a31ba3abba
a3a31baaba2b2a3a2ba3b2b3abb2ab3a2b2a2b3a3b3
ba2ba2ba3b2a2bb2a3b3a2bab2b3a31b2ab3ab3aa2a3
b2ab2ab2a2b3a3b2a3b3a3b2b3a1bab3a2aba2a2ba3b
b3b3b3aa2b3a2a3ba2b3a31ba3b2a2abb2a3bab2b2a
ba3ba3bb2abab2a2b3a3ba2b2a3b3a3b2b3a1b3a2aa2
b2a2b2a2b2a3b3a2b2b3a31b2ab3abb3aa2baa3ba2ba3
b3ab3ab3a2ab3a3a2ba3b3a3bb2a1bab2a2ba2b2a3b2
b2a3b2a3b2b3ab2ab3a2ab2a2b3a3a2ba3b3a3b1baba2
b3a2b3a2b3a31b3abb3aa2bab2a3ba2b2aba3b2a2b2a3
b3a3b3a3b3a3b3a1bab3a2aba2b2a3a2ba3b2bb2ab2a2

Right Cayley graph

Left Cayley graph

Others with same cardinality

26 unique, 170 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 | aaaa=b, bbbb=1〉 Isomorphic to ℤ16 67 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
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

5 total

Length:Presentation:
10〈a, b | aba=b, abbabb=1〉
10〈a, b | aba=b, abbbba=1〉
10〈a, b | aba=b, baabbb=1〉
10〈a, b | aba=b, babbab=1〉
10〈a, b | aba=b, bbaabb=1〉