#14981 ⟨a, b | aaa=bb, aabaab=1⟩

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Properties

Elements

Elements in the center commute with all other elements.
The order of x is the least n such that xn = 1.

Complete rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
  1. a21 ⇒ 1
  2. ab ⇒ ba8
  3. b2 ⇒ a3 
# ab:aaa=bb,aabaab=1 a/b
aaaaaaaaaaaaaaaaaaaaa=1
ab=baaaaaaaa
bb=aaa

Right Cayley graph

Left Cayley graph

Others with same cardinality

2 unique, 5 total

Σ#PresentationDescriptionRelated
106101⟨a, b | aab=a, bbbbbb=1⟩Finite non-commutative monoid with 42 elements3 iso
1120647⟨a, b | ab=aa, bbbbbb=b⟩Finite non-commutative monoid with 42 elements

Other isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

7 total

Σ#PresentationMapping
1114989⟨a, b | aaa=bb, abaaba=1⟩φ(a) = a, φ(b) = b
1126093⟨a, b | aa=1, abbabbbbb=1⟩φ(a) = baa, φ(b) = a
1126108⟨a, b | aa=1, abbbbbabb=1⟩φ(a) = baa, φ(b) = a
1126158⟨a, b | aa=1, babbabbbb=1⟩φ(a) = baa, φ(b) = a
1126162⟨a, b | aa=1, babbbbbab=1⟩φ(a) = baa, φ(b) = a
1126175⟨a, b | aa=1, bbabbabbb=1⟩φ(a) = baa, φ(b) = a
1126704⟨a, b | aa=1, bbabbbbb=a⟩φ(a) = baa, φ(b) = a