Nuclear magnetism inn-doped semiconductors with a positive hyperfine constant is revisited. Two kindsof nuclear magnetic ordering can be induced by resident electrons in a deeply cooled nuclear spin system.At positive nuclear spin temperature below a critical value, randomly oriented nuclear spin polarons similarto that predicted by Merkulov [Phys. Solid State40, 930 (1998)] should emerge. These polarons are orientedrandomly, and within each polaron, nuclear and electron spins are aligned antiferromagnetically. At negativenuclear spin temperature below a critical value, we predict another type of magnetic ordering—a dynamicallyinduced nuclear ferromagnet. This is a long-range ferromagnetically ordered state involving both electrons andnuclei. It can form if electron spin relaxation is dominated by the hyperfine coupling, rather than by the spin-orbitinteraction. Application of the theory to then-doped GaAs suggests that ferromagnetic order may be reached atexperimentally achievable nuclear spin temperatureN≈−0.5μK and lattice temperatureTL≈5K.