Back

〈a, b | baab=a, bbbb=1〉

Monoid presentation of length 9

Properties

Completion parameters

Complete rewriting system

  1. a13 ⇒ a
  2. aba12 ⇒ ab
  3. a3b ⇒ ba3
  4. ba2b ⇒ a
  5. ab2 ⇒ baba2
  6. a(ab)2 ⇒ b2a
  7. b3a ⇒ a2b
  8. b(ab)2 ⇒ aba10
  9. b4 ⇒ 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 | 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
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 | abbb=baa, bbbb=1〉
11〈a, b | aaaa=1, aabba=ab〉