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〈a, b | aba=bb, aaaa=1〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. b13 ⇒ b
  2. bab12 ⇒ ba
  3. b3a ⇒ ab3
  4. aba ⇒ b2
  5. ba2b12 ⇒ ba2
  6. bab2a ⇒ a2b5
  7. b2a2 ⇒ ab2ab10
  8. a3b ⇒ bab11
  9. ba3 ⇒ b2ab10
  10. ba2b2a ⇒ a2b2ab5
  11. a4 ⇒ 1

Idempotents

2 elements

Right Cayley graph

Left Cayley graph

Others with same cardinality

6 unique, 10 total

Length:Presentation:Description:Related:
9 〈a, b | baab=a, bbbb=1〉 Finite non-commutative monoid with 100 elements 2 isomorphic
10 〈a, b | bab=aba, aaaa=1〉 Finite non-commutative monoid with 100 elements
10 〈a, b | aaaa=1, ababa=b〉 Finite non-commutative monoid with 100 elements
11 〈a, b | abba=bab, bbbb=1〉 Finite non-commutative monoid with 100 elements
11 〈a, b | aaaaa=1, ababbb=1〉 Finite non-Abelian group with 100 elements 2 isomorphic
11 〈a, b | aaaa=1, abaaba=b〉 Finite non-commutative monoid with 100 elements

Other isomorphic instances

2 total

Length:Presentation:
11〈a, b | babb=aab, bbbb=1〉
11〈a, b | aaaa=1, aaabb=ba〉