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〈a, b | aaa=1, bababb=a〉

Monoid presentation of length 10

Properties

Completion parameters

Inverses of generators

Complete rewriting system

  1. b12 ⇒ 1
  2. b3a ⇒ ab3
  3. aba ⇒ b2ab7
  4. ba2 ⇒ ab2ab11
  5. (b2a)2 ⇒ a2b4
  6. a3 ⇒ 1
  7. a2b2a ⇒ bab5

Right Cayley graph

Left Cayley graph

Others with same cardinality

6 unique, 21 total

Length:Presentation:Description:Related:
9 〈a, b | aaa=1, babbb=a〉 Finite non-Abelian group with 84 elements 2 isomorphic, 1 anti-isomorphic
10 〈a, b | aaa=1, aababbb=1〉 Finite non-Abelian group with 84 elements 2 isomorphic, 4 anti-isomorphic
10 〈a, b | aaa=1, babbb=ab〉 Finite non-commutative monoid with 84 elements 3 isomorphic
10 〈a, b | aaa=1, bbabb=ab〉 Finite non-commutative monoid with 84 elements 3 isomorphic
11 〈a, b | aaa=1, baababb=a〉 Finite non-Abelian group with 84 elements
11 〈a, b | aaa=1, baabbab=a〉 Finite non-Abelian group with 84 elements

Other isomorphic instances

5 total

Length:Presentation:
11〈a, b | aaa=1, aabababb=1〉
11〈a, b | aaa=1, abababba=1〉
11〈a, b | aaa=1, ababbaab=1〉
11〈a, b | aaa=1, abbaabab=1〉
11〈a, b | aaa=1, baababab=1〉

Other anti-isomorphic instances

3 total

Length:Presentation:
11〈a, b | aaa=1, aabbabab=1〉
11〈a, b | aaa=1, abaabbab=1〉
11〈a, b | aaa=1, ababaabb=1〉