#3624 ⟨a, b, c | aaa=1, abccb=1⟩

Properties

Sum of relation sides is 8
Infinite non-Abelian group
Element ba² has infinite order
Inverses of generators:
- a^-1 = a²
- b^-1 = abc²
- c^-1 = cbab
Reduced group presentation: ⟨a, b | aabbaabbaabb⟩
- Isomorphism: φ(a) = abba, φ(b) = a^-1, φ(c) = b^-1

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

# abc:aaa=1,abccb=1 acb - -
aaa=1
ccba=abcc
babc=cbab
bccb=aa
bccaa=aaccb

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

3 total

Σ	#	Presentation	Mapping
8	3637	⟨a, b, c \| aaa=1, baccb=1⟩	φ(a) = abccabcccbabcbab, φ(b) = b, φ(c) = c
8	3649	⟨a, b, c \| aaa=1, bcacb=1⟩	φ(a) = cbababccabcccbab, φ(b) = b, φ(c) = c
8	4152	⟨a, b, c \| aaa=1, bccb=a⟩	φ(a) = abcccbabcbababcc, φ(b) = abcc, φ(c) = cbab