V članku predstavimo uvod v teorijo inverznih polgrup. Poseben poudarek je na simetrični inverzni polgrupi, ki jo sestavljajo vse parcialno definirane injektivne preslikave iz množice vase, ter na ...inverznih polgrupah, ki jih dobimo iz grup, ki parcialno delujejo na polmrežah s pomočjo konstrukcije semidirektnega produkta. Podrobno opišemo nekaj pomembnih primerov inverznih polgrup, ki nastanejo s pomočjo omenjene konstrukcije. Bralcu tako predstavimo ne le uvod v osnove teorije inverznih polgrup, pač pa tudi uvod v področje trenutnih aktivnih raziskav iz inverznih polgrup in njihovih posplošitev.
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