Nech (G,•) je grupa:
a) Dokážte, že prienik ľubovoľného neorazdneho systému podgrup grupy (G,•) je opäť podgrupou grupy (G,•)
b) Ukážte, že zjednotením dvoch podgrup grupy (G,•) (všeobecne) nieje podgrupou grupy (G,•).
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