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〈a, b | aa=1, ababa=bbb〉

Monoid presentation of length 10

Properties

Completion parameters

Complete rewriting system

  1. a2 ⇒ 1
  2. (ba)2 ⇒ ab3
  3. b3a ⇒ (ab)2
  4. b2ab3 ⇒ abab2a
  5. bab7 ⇒ aba(b2a)2
  6. b10 ⇒ a(b2a)3
  7. ba(b2a)3 ⇒ a(b2a)3b

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
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
11 〈a, b | aa=1, abababa=bb〉 Finite non-commutative monoid with 64 elements 2 isomorphic

Other isomorphic instances

2 total

Length:Presentation:
10〈a, b | aa=1, abbba=bab〉
10〈a, b | aa=1, baba=abbb〉