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〈a, b | aaaa=1, aababb=1〉

Monoid presentation of length 10

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. b12 ⇒ 1
  2. b4a ⇒ ab4
  3. a2 ⇒ bab2
  4. aba ⇒ b3ab
  5. ab2a ⇒ b2ab3
  6. ab3a ⇒ b9

Right Cayley graph

Left Cayley graph

Others with same cardinality

11 unique, 34 total

Length:Presentation:Description:Related:
9 〈a, b | aaba=b, bbbb=1〉 Finite non-Abelian group with 60 elements 4 isomorphic, 5 anti-isomorphic
10 〈a, b | aaba=bb, bbbb=1〉 Finite non-Abelian group with 60 elements 2 isomorphic
10 〈a, b | aaaa=1, baabb=a〉 Finite non-Abelian group with 60 elements
11 〈a, b | baabb=a, bbbbb=1〉 Finite non-commutative monoid with 60 elements
11 〈a, b | aaba=bb, aaaaa=1〉 Finite non-commutative monoid with 60 elements
11 〈a, b | aabb=ba, aaaaa=1〉 Finite non-commutative monoid with 60 elements
11 〈a, b | baa=abb, aaaaa=1〉 Finite non-commutative monoid with 60 elements
11 〈a, b | aaba=b, abbabb=1〉 Finite non-Abelian group with 60 elements 2 isomorphic
11 〈a, b | aaaa=1, baabab=a〉 Finite non-Abelian group with 60 elements
11 〈a, b | aa=1, ababbabbb=1〉 Finite non-Abelian group with 60 elements 4 isomorphic
11 〈a, b | aa=1, ababbbabb=1〉 Finite non-Abelian group with 60 elements 6 isomorphic

Other isomorphic instances

3 total

Length:Presentation:
10〈a, b | aaaa=1, ababba=1〉
10〈a, b | aaaa=1, abbaab=1〉
10〈a, b | aaaa=1, baabab=1〉