Let G be a group, and let {H | AE A} be a set of subgroups...

Transcribed Image Text:

Let G be a group, and let {H | AE A} be a set of subgroups of G. Show that W = x^Hx is a subgroup of G. (Caution: The set A may be of any cardinality. It is not necessarily finite, or even countable. Your argument should be for the general case, not for the finite or countable case.) Let G be a group, and let {H | AE A} be a set of subgroups of G. Show that W = x^Hx is a subgroup of G. (Caution: The set A may be of any cardinality. It is not necessarily finite, or even countable. Your argument should be for the general case, not for the finite or countable case.)