theorem Th25: :: GRNILP_1:25

for G, H being strict Group
for h being Homomorphism of G,H
for G1 being strict Subgroup of G
for G2 being strict normal Subgroup of G
for H1 being strict Subgroup of Image h
for H2 being strict normal Subgroup of Image h st G2 is strict Subgroup of G1 & G1 ./. ((G1,G2) `*`) is Subgroup of center (G ./. G2) & H1 = h .: G1 & H2 = h .: G2 holds
H1 ./. ((H1,H2) `*`) is Subgroup of center ((Image h) ./. H2)