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〈a, b | aa=1, abababa=bb〉

Monoid presentation of length 11

Properties

Completion parameters

Complete rewriting system

  1. b10 ⇒ b4
  2. bab8 ⇒ bab2
  3. b2ab7 ⇒ b2ab
  4. b3a ⇒ ab3
  5. a2 ⇒ 1
  6. b(ab)2 ⇒ ab2a
  7. bab2ab6 ⇒ bab2a
  8. b(ba)2 ⇒ bab2ab5
  9. (b2a)2 ⇒ abab4

Idempotents

2 elements

Right Cayley graph

Left Cayley graph

Others with same cardinality

6 unique, 13 total

Length:Presentation:Description:Related:
9 〈a, b | aab=ba, bbbb=1〉 Finite non-commutative monoid with 64 elements 2 isomorphic
10 〈a, b | abab=ba, bbbb=1〉 Finite non-commutative monoid with 64 elements
10 〈a, b | aaaa=1, ababbb=1〉 Finite non-Abelian group with 64 elements 2 isomorphic
10 〈a, b | aa=1, ababa=bbb〉 Finite non-commutative monoid with 64 elements 2 isomorphic
11 〈a, b | baab=abb, bbbb=1〉 Finite non-commutative monoid with 64 elements 1 isomorphic
11 〈a, b | aaaa=1, abaab=ba〉 Finite non-commutative monoid with 64 elements

Other isomorphic instances

2 total

Length:Presentation:
11〈a, b | aa=1, ababab=bba〉
11〈a, b | aa=1, babab=abba〉