#7548 ⟨a, b | aaa=1, bbabbb=a⟩

Up:Monoids with two generators and two relations
Prev:#7547 ⟨a, b | aaa=1, bbaabb=b⟩
Next:#7549 ⟨a, b | aaa=1, bbabbb=b⟩

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. b35 ⇒ 1
  2. ba ⇒ ab16
  3. a3 ⇒ 1 
# ab:aaa=1,bbabbb=a b/a
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=1
ba=abbbbbbbbbbbbbbbb
aaa=1

Right Cayley graph

Left Cayley graph

Other isomorphic instances

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

9 total

Σ#PresentationMapping
1121170⟨a, b | aaa=1, aabbabbb=1⟩φ(a) = a, φ(b) = b
1121173⟨a, b | aaa=1, aabbbabb=1⟩φ(a) = aa, φ(b) = b
1121205⟨a, b | aaa=1, abbaabbb=1⟩φ(a) = aa, φ(b) = b
1121209⟨a, b | aaa=1, abbabbba=1⟩φ(a) = a, φ(b) = b
1121212⟨a, b | aaa=1, abbbaabb=1⟩φ(a) = a, φ(b) = b
1121232⟨a, b | aaa=1, baabbabb=1⟩φ(a) = a, φ(b) = b
1121233⟨a, b | aaa=1, baabbbab=1⟩φ(a) = aa, φ(b) = b
1121241⟨a, b | aaa=1, babbaabb=1⟩φ(a) = aa, φ(b) = b
1121774⟨a, b | aaa=1, babbabb=a⟩φ(a) = a, φ(b) = ab