#2839 ⟨a, b | aaaaabbbbba=1⟩

Properties

Sum of relation sides is 11
Infinite non-Abelian group
Element a⁴ba has infinite order
Inverses of generators:
- a^-1 = a⁵d
- b^-1 = b⁴c
- c^-1 = d
- d^-1 = c
Reduced group presentation: ⟨a, b | aaaaaabbbbb⟩
- Isomorphism: φ(a) = a, φ(b) = b

Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

# ab:aaaaabbbbba=1 abcd aaaaaa=c,bbbbb=d magic:0
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
bbbbb=d
aaaaaa=c

1 unique, 1 total

Σ	#	Presentation	Properties
11	5436	⟨a, b \| aaaaaa=bbbbb⟩	Can Inf

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

4 total

Σ	#	Presentation	Mapping
11	2896	⟨a, b \| aaaabbbbbaa=1⟩	φ(a) = a, φ(b) = b
11	2898	⟨a, b \| aaaabbbbbba=1⟩	φ(a) = b, φ(b) = a
11	2998	⟨a, b \| aaabbbbbaaa=1⟩	φ(a) = a, φ(b) = b
11	3002	⟨a, b \| aaabbbbbbaa=1⟩	φ(a) = b, φ(b) = a