#1336 ⟨a, b | aaaabbbbba=1⟩

Properties

Sum of relation sides is 10
Infinite non-Abelian group
Element a³ba has infinite order
Inverses of generators:
- a^-1 = a⁴d
- b^-1 = b⁴c
- c^-1 = d
- d^-1 = c
Reduced group presentation: ⟨a, b | aaaaabbbbb⟩
- 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:aaaabbbbba=1 abcd aaaaa=c,bbbbb=d magic:0
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
aaaaa=c
bbbbb=d

1 unique, 1 total

Σ	#	Presentation	Properties
10	2776	⟨a, b \| bbbbb=aaaaa⟩	Can Inf

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

1 total

Σ	#	Presentation	Mapping
10	1388	⟨a, b \| aaabbbbbaa=1⟩	φ(a) = a, φ(b) = b