#2791 ⟨a, b | aaaaaaabbba=1⟩

Properties

Sum of relation sides is 11
Infinite non-Abelian group
Element a⁶ba has infinite order
Inverses of generators:
- a^-1 = a⁷d
- b^-1 = b²c
- c^-1 = d
- d^-1 = c
Reduced group presentation: ⟨a, b | aaaaaaaabbb⟩
- 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:aaaaaaabbba=1 abcd aaaaaaaa=c,bbb=d magic:0
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
bbb=d
aaaaaaaa=c

1 unique, 1 total

Σ	#	Presentation	Properties
11	4366	⟨a, b \| aaaaaaaa=bbb⟩	Can Inf

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

4 total

Σ	#	Presentation	Mapping
11	2805	⟨a, b \| aaaaaabbbaa=1⟩	φ(a) = a, φ(b) = b
11	2833	⟨a, b \| aaaaabbbaaa=1⟩	φ(a) = a, φ(b) = b
11	2884	⟨a, b \| aaaabbbaaaa=1⟩	φ(a) = a, φ(b) = b
11	3168	⟨a, b \| aabbbbbbbba=1⟩	φ(a) = b, φ(b) = a