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This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group Definition
The free group of rank two, also written as , is defined as the free group on a generating set of size two. is the smallest possible rank for a free non-abelian group (the free groups of rank and are respectively the trivial group and the group of integers).
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The free group of rank two is a SQ-universal group. In particular, it has subgroups that are free of every finite rank as well as a free subgroup of countable rank.
Arithmetic functions
Group properties
GAP implementation
The free group of rank two can be constructed using GAP with the GAP:FreeGroup command:
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Further, the generators can also be referred to. For instance, if we use:
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Then the two generators can be referred to as and .
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