Free product of groups

The free product is the coproduct in . #m/def/group Let be groups. Then the free product has finite strings of elements taken from any as its words with all the identities considered the same, which may then be reduced using the group laws of each . A reduced word is therefore a word where no adjacent elements come from the same group. Reduced words may be regarded as the elements of the free product group

A more general construction is the Amalgamated free product.

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