Section QuotientInternalProd.
Variables (gT : finGroupType) (G K H M : {group gT}).
Hypothesis nMG: G \subset 'N(M).
Canonical setX_group H1 H2 := Group (group_setX H1 H2).
Definition pairg1 x : gT1 * gT2 := (x, 1).
Definition pair1g x : gT1 * gT2 := (1, x).

Lemma isog_setX1 (H1 : {group gT1}) : isog H1 (setX H1 1).