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〈a, b | aaaa=1, ababa=b〉

Monoid presentation of length 10

Properties

Completion parameters

Complete rewriting system

  1. b9 ⇒ b
  2. bab8 ⇒ ba
  3. b2a ⇒ ab2
  4. ba2b8 ⇒ ba2
  5. a3b ⇒ (ba)2
  6. a(ba)2 ⇒ b
  7. ba3 ⇒ (ab)2
  8. a4 ⇒ 1
  9. (aba)2 ⇒ ba2b7
  10. (ba2)2 ⇒ a2ba2b5

Idempotents

2 elements

Right Cayley graph

Left Cayley graph

Others with same cardinality

6 unique, 12 total

Length:Presentation:Description:Related:
9 〈a, b | baab=a, bbbb=1〉 Finite non-commutative monoid with 100 elements 2 isomorphic
9 〈a, b | aba=bb, aaaa=1〉 Finite non-commutative monoid with 100 elements 2 isomorphic
10 〈a, b | bab=aba, aaaa=1〉 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