On monoids of injective partial cofinite selfmapsGutik, Oleg (Avtor) Repovš, Dušan (Avtor) mathematicsbicyclic semigroupsemigroup of bijective partial transformationscongruencesymmetric groupgroup congruencesemidirect productWe study the semigroup ▫$\mathscr{I}^{\mathrm{cf}}_\lambda$▫ of injective partial cofinite selfmaps of an infinite cardinal ▫$\lambda$▫. We show that ▫$\mathscr{I}^{\mathrm{cf}}_\lambda$▫ is a bisimple inverse semigroup and each chain of idempotents in ▫$\mathscr{I}^{\mathrm{cf}}_\lambda$▫ is contained in a bicyclic subsemigroup of ▫$\mathscr{I}^{\mathrm{cf}}_\lambda$▫, we describe the Green relations on ▫$\mathscr{I}^{\mathrm{cf}}_\lambda$▫ and we prove that every non-trivial congruence on ▫$\mathscr{I}^{\mathrm{cf}}_\lambda$▫ is a group congruence. Also, we describe the structure of the quotient semigroup ▫$\mathscr{I}^{\mathrm{cf}}_\lambda/\sigma$▫, where ▫$\sigma$▫ is the least group congruence on ▫$\mathscr{I}^{\mathrm{cf}}_\lambda$▫.20152019-09-26 10:24:20Članek v reviji111234UDK: 512.536ISSN pri članku: 0139-9918DOI: http://dx.doi.org/10.1515/ms-2015-0067COBISS_ID: 17538393OceCobissID: 27357184sl