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〈a, b | aaaa=a, abba=b〉

Monoid presentation of length 10

Properties

Completion parameters

Complete rewriting system

  1. ba2 ⇒ ab2
  2. b2a ⇒ a2b
  3. a4 ⇒ a
  4. a3b ⇒ b
  5. bab2 ⇒ a2ba
  6. b5 ⇒ a(ba)2
  7. (ba)3 ⇒ (ab)3

Idempotents

3 elements

Right Cayley graph

Left Cayley graph

Others with same cardinality

7 unique, 8 total

Length:Presentation:Description:Related:
10 〈a, b | aaaa=a, abbb=b〉 Finite non-commutative monoid with 28 elements
10 〈a, b | aaab=b, babb=a〉 Finite non-commutative monoid with 28 elements
10 〈a, b | aaab=b, bbab=a〉 Finite non-commutative monoid with 28 elements
10 〈a, b | aaba=b, babb=a〉 Finite non-commutative monoid with 28 elements
10 〈a, b | aaba=b, bbab=a〉 Finite non-commutative monoid with 28 elements
11 〈a, b | aaaa=a, aabbb=b〉 Finite non-commutative monoid with 28 elements 1 isomorphic
11 〈a, b | aaaa=a, ababa=b〉 Finite non-commutative monoid with 28 elements