#1086 ⟨a, b, c | aa=1, abccb=1⟩

Properties

Sum of relation sides is 7
Infinite non-Abelian group
Element ba has infinite order
Inverses of generators:
- a^-1 = a
- b^-1 = abc²
- c^-1 = cbab
Reduced group presentation: ⟨a, b | aabbaabb⟩
- 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:aa=1,abccb=1 acb - -
aa=1
ccba=abcc
babc=cbab
bcca=accb
bccb=a

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

5 total

Σ	#	Presentation	Mapping
7	1099	⟨a, b, c \| aa=1, baccb=1⟩	φ(a) = abccabcccbabcbab, φ(b) = b, φ(c) = c
7	1111	⟨a, b, c \| aa=1, bcacb=1⟩	φ(a) = cbababccabcccbab, φ(b) = b, φ(c) = c
7	1272	⟨a, b, c \| aa=1, bccb=a⟩	φ(a) = abcccbabcbababcc, φ(b) = abcc, φ(c) = cbab
8	2246	⟨a, b, c \| abab=1, bcac=1⟩	φ(a) = cbababccabcc, φ(b) = cbab, φ(c) = bc
8	2528	⟨a, b, c \| aab=c, bcbc=1⟩	φ(a) = b, φ(b) = abccabcccbab, φ(c) = cbab