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it is known that given two subgroups [itex]H\subset G[/itex], and [itex]K\subset G[/itex] of some group G, then we have that:

1) H, K arenormalsubgroups of G

2) [itex]H\cap K[/itex] is trivial

aresufficientconditions for H and K tocommute.

Moreover we have that:

H, K commute [itex]\Rightarrow[/itex] H, K are normal.

In fact, conditions 1) and 2) together are notnecessaryconditions for commutativity because there exist subgroups that are commutative but donothave trivial intersection (it is posible to find examples).

My question is: is it possible to keep condition 1) and instead replace only 2) with some weaker condition that would make 1),2) necessary and sufficient conditions for commutativity?

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# Question on conditions for commutativity of subgroups

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