#298 ⟨a, b | aaabbbba=1⟩

Properties

Sum of relation sides is 8
Infinite non-Abelian group
Element a²ba has infinite order
Inverses of generators:
- a^-1 = a³d
- b^-1 = b³c
- c^-1 = d
- d^-1 = c
Reduced group presentation: ⟨a, b | aaaabbbb⟩
- 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:aaabbbba=1 abcd aaaa=c,bbbb=d magic:0
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
aaaa=c
bbbb=d

2 unique, 2 total

Σ	#	Presentation	Properties
8	594	⟨a, b \| bbbb=aaaa⟩	Can Inf
10	2334	⟨a, b \| abababa=bbb⟩	Can Inf

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

1 total

Σ	#	Presentation	Mapping
8	318	⟨a, b \| aabbbbaa=1⟩	φ(a) = a, φ(b) = b