n lgbr, trnsfrmtn smgrp (r cmpstn smgrp) s cllctn f trnsfrmtns (fnctns frm st t tslf) tht s clsd ndr fnctn cmpstn. f t nclds th dntty fnctn, t s mnd, clld trnsfrmtn (r cmpstn) mnd. Ths s th smgrp nlg f prmttn grp.
trnsfrmtn smgrp f st hs ttlgcl smgrp ctn n tht st. Sch ctns r chrctrzd by bng fthfl, .., f tw lmnts f th smgrp hv th sm ctn, thn thy r ql.
n nlg f Cyly's thrm shws tht ny smgrp cn b rlzd s trnsfrmtn smgrp f sm st.
n tmt thry, sm thrs s th trm trnsfrmtn smgrp t rfr t smgrp ctng fthflly n st f "stts" dffrnt frm th smgrp's bs st. Thr s crrspndnc btwn th tw ntns.