let g be a group, and h a subgroup of g. how many of the left cosets of h are subgroups of g? does the answer to this question always have to be the same, or can it vary according to the group and the subgroup?
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let g be a group, and h a subgroup of g. how many of the left cosets of h are subgroups of g? does the answer to this question always have to be the same, or can it vary according to the group and the subgroup?
answer :There are four left cosets of H: H itself, 1 + H, 2 + H, and 3 + H (written using additive notation since this is the additive group). Together they partition the entire group G into equal-size, non-overlapping sets.