#1289 ⟨a, b | aaaaaabbba=1⟩

Properties

Sum of relation sides is 10
Infinite non-Abelian group
Element a⁵ba has infinite order
Inverses of generators:
- a^-1 = a⁶d
- b^-1 = b²c
- c^-1 = d
- d^-1 = c
Reduced group presentation: ⟨a, b | aaaaaaabbb⟩
- 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:aaaaaabbba=1 abcd aaaaaaa=c,bbb=d magic:0
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
bbb=d
aaaaaaa=c

2 unique, 2 total

Σ	#	Presentation	Properties
10	2096	⟨a, b \| aaaaaaa=bbb⟩	Can Inf
11	5433	⟨a, b \| aaaaaa=babab⟩	Can Inf

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

3 total

Σ	#	Presentation	Mapping
10	1303	⟨a, b \| aaaaabbbaa=1⟩	φ(a) = a, φ(b) = b
10	1330	⟨a, b \| aaaabbbaaa=1⟩	φ(a) = a, φ(b) = b
10	1474	⟨a, b \| aabbbbbbba=1⟩	φ(a) = b, φ(b) = a