Every element of a free product has a unique expression in which each is a nonidentity element of one factor and adjacent syllables belong to different factors. The identity corresponds to the empty word.
A syllable is a nonidentity element of one factor in a free product word. A reduced normal form has successive syllables in different factors; its syllable length is the number of these elements. This length records factor elements, rather than letters in a chosen generating set.

Ancestors (10)

  1. Normal form for free groups and free product of groups
  2. Free product
  3. Amalgamated free product
  4. Seifert-van Kampen theorem
  5. Fundamental group
  6. Algebraic topology
  7. Geometry and topology
  8. Area of mathematics
  9. Mathematics
  10. Home

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