WebAug 17, 2024 · Example 15.2.5: Cosets in a Direct Product. Consider F = (Z4 × Z2) / H, where H = {(0, 0), (0, 1)}. Since Z4 × Z2 is of order 8, each element of F is a coset … Let H be a subgroup of the group G whose operation is written multiplicatively (juxtaposition denotes the group operation). Given an element g of G, the left cosets of H in G are the sets obtained by multiplying each element of H by a fixed element g of G (where g is the left factor). In symbols these are, The right cosets are defined similarly, except that the element g is now a right factor, that is,

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