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Left cosets partition a group

36 bytes added, 21:38, 4 May 2010
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# The left cosets of <math>H</math>, namely <math>gH, g \in G</math>, form a partition of the group <math>G</math>. In other words, <math>G</math> is a disjoint union of left cosets of <math>H</math>.
# The relation <math>a \sim b \iff a \in bH</math> is an equivalence relation on <math>G</math>
# For every <math>g \in G</math>, there is ''exactly'' one left coset of <math>H</math> in <math>G</math> containing <math>g</math>.
# If <math>aH</math> and <math>bH</math> are left cosets of <math>H</math> in <math>G</math>, then either <math>aH = bH</math> or <math>aH \cap bH</math> is empty.
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