How get repeated elements from two lists

Question

How to write a code that takes an certain element related to a given subset in a LIST 2, that occurs also in a LIST 1?

for example, there are two lists:

    LIST 1= {"Cl Berkeley 58 ", "NGC 7801 ", "C 2359+643 ", "Cl Berkeley 59 ", \
"Cl Berkeley 104 ", "Cl Blanco 1 ", "C 0001+557 ", "NGC 7826 ", "C \
0005+611 ", "[KPS2012] MWSC 0018 ", "Cl Berkeley 1 ", "C 0007+609 ", \
"Cl Berkeley 60 ", "C 0019+641 ", "[KPS2012] MWSC 0037 ", "C 0022+623 \
", "NGC 103 ", "Cl Berkeley 2 ", "NGC 110 ", "[KPS2012] MWSC 0046 ", \
"NGC 129 ", "C 0027+577 ", "NGC 133 ", "NGC 136 ", "C 0029+628 ", "Cl \
King 15 ", "NGC 146 ", "DSH J0033.1+6507 ", "NGC 189 ", "Cl Stock 24 \
", "Cl Dias 1 ", "NGC 225 ", "C 0040+598 ", "C 0040+639 ", "Cl \
Berkeley 4 ", "NGC 188 ", "Cl Berkeley 61 ", "C 0047+638 ", "C \
0048+579 ", "IC 1590 ", "Cl Berkeley 62 ", "Cl Czernik 3 ", "NGC 358 \
", "NGC 366 ", "NGC 381 ", "C 0109+620 ", "NAME HIP 5671 CLUSTER ", \
"NGC 433 ", "NGC 436 ", "NGC 457 ", "[KPS2012] MWSC 0120 ", "NGC 559 \
", "M 103 ", "Cl Czernik 4 ", "C 0132+610 ", "NGC 609 ", "NGC 637 ", \
"NGC 657 ", "NGC 654 ", "NGC 659 ", "C 0144+717 ", "NGC 663 ", "Cl \
Berkeley 5 ", "Cl Berkeley 6 ", "IC 166 ", "C 0149+568 ", "Cl \
Berkeley 7 ", "Cl Czernik 5 ", "NGC 752 ", "NGC 744 ", "NGC 743 ", \
"Cl Berkeley 8 ", "Cl Czernik 6 ", "Cl Czernik 7 ", "C 0200+642 ", \
"[KPS2012] MWSC 0165 ", "Riddle 4 ", "C 0211+590 ", "NGC 869 ", "C \
0215+580 ", "Cl Berkeley 63 "....} 



  LIST2 = `{{"Cl fug k9 ", {"C 2357+606", "OCl 277.0", "[KPR2004b] 1", 
   "Cl Berkeley 58", 
   "[KPS2012] MWSC 0001"}}, {"* gam Peg ", {"2MASS J00131414+1511008", "FK5 7", "PLX 33", 
      "* 88 Peg", "* gam Peg", "AAVSO 0008+14", "AG+14 11", "BD+14 14", 
      "CCDM J00132+1511A", "CSI+14 14 1", "CSV 100009", "GC 238", 
      "GCRV 105", "GEN# +1.00000886", "GSC 01179-01775", "HD 886", 
      "HGAM 5", "HIC 1067", "HIP 1067", "HR 39", "IDS 00080+1438 A", 
      "IRAS 00106+1454", "JP11 353", "N30 32", "NAME ALGENIB", "PHL 734", 
      "PMC 90-93 6", "PPM 116243", "ROT 69", "SAO 91781", "SKY# 390", 
      "SRS 30007", "TD1 78", "TYC 1179-1775-1", "UBV 128", "V* gam Peg", 
      "uvby98 100000886 V", "ALS 15090", "PLX 33.00", 
      "WDS J00132+1511A"}}, {"* zet Per ", {"PLX 856", "[GBA2007] 79", 
      "XEST 27-079", "* zet Per", "* 44 Per", "2E 902", "ADS 2843 A", 
      "AG+31 368", "BD+31 666", "CCDM J03541+3153A", "CSI+31 666 1", 
      "CSV 100357", "FK5 144", "GC 4688", "GCRV 2230", 
      "GEN# +1.00024398A", "GSC 02361-02820", "HD 24398", "HGAM 301", 
      "HIC 18246", "HIP 18246", "HR 1203", "IDS 03478+3135 A", 
      "IRC +30068", "JP11 828", "MCW 252", "N30 800", "NSV 1397", 
      "PMC 90-93 104", "PPM 68893", "ROT 574", "SAO 56799", "SKY# 5968", 
      "SRS 30144", "SV* ZI 260", "TD1 2623", "TYC 2361-2820-1", 
      "UBV 3778", "YPAC 14", "[C93] 149", "[KSP2003] G162.2896-16.6902", 
      "uvby98 100024398 A", "ALS 14763", "1RXS J035407.3+315255", 
      "2E 0350.9+3144", "[KSP2003] J035408.02+315300.2", 
      "2XMM J035407.8+315300", 
      "WDS J03541+3153A"}}, {"* eps Per ", {"PLX 869", "SBC9 2402", 
      "* 45 Per", "* eps Per", "AAVSO 0351+39", "ADS 2888 A", "AG+39 463",
       "ALS 7825", "BD+39 895", "CCDM J03579+4001A", "CEL 373", 
      "CSI+39 895 1", "CSV 100363", "EUVE J0357+40.0", "FK5 147", 
      "GC 4759", "GCRV 2266", "GEN# +1.00024760J", "GEN# +1.00024760A", 
      "GSC 02868-01623", "HD 24760", "HGAM 307", "HIC 18532", "HIP 18532",
       "HR 1220", "IDS 03511+3943 A", "JP11 837", "LS V +39 1", "MCW 257",
       "N30 815", "NSV 1423", "PMC 90-93 105", "PPM 46661", "ROT 3497", 
      "SAO 56840", "SKY# 6055", "SRS 30147", "SV* ZI 263", "TD1 2676", 
      "TYC 2868-1623-1", "UBV 3847", "V* eps Per", "uvby98 100024760 ABV",
       "WDS J03579+4001A", "IRAS 03544+3952", 
      "AKARI-IRC-V1 J0357512+400036", "PMSC 03511+3943A", 
      "PMSC 03511+3943Aabc"}}}

So in the LIST 1 is a set of strings names, LIST 2 is a set of sublists for certains string names, that could be the same OR NOT as in the LIST 1.

I need the following rationalite: If name 1 in the LIST 1, is the same as name "j" in the sublist of LIST 2, then take the element name "i" related to that sublist:

    (*   LIST 1 there is "Cl Berkeley 58 " , 
    and the its related "element" in the LIST 2 is:
     {"Cl fug k9  ", {"C 2357+606", "OCl 277.0", "[KPR2004b] 1", 
           "Cl Berkeley 58", 
           "[KPS2012] MWSC 0001"}} ,  
so take the element name "i" = "Cl fug k9  "*)

So I need to make a list of names that is composed by these "intersection names" , as:

 ListResulting={"Cl fug k9 ",............}

Summarizing, I am trying to filter the redundancies names in different catalogues,using the LIST1 as my reference catalogue and build a final one that includes all names with no redundancies. The sublists in LIST 2 are different names of the same object (name "i"). And I ll have to repeat these filtering for many list that has its own set of sublists, but always using the LIST 1 as the comparing list.

Answer 1

You can use Select:

With[{l1 = Map[StringTrim, LIST1, {-1}], l2 = Map[StringTrim, LIST2, {-1}]},
    Select[l2, Intersection[l1, #[[2]]] != {} &]]
(* {{"Cl fug k9", {"C 2357+606", "OCl 277.0", "[KPR2004b] 1", "Cl Berkeley 58", 
     "[KPS2012] MWSC 0001"}}} *)

Or Pick

With[{l1 = Map[StringTrim, LIST1, {-1}], l2 = Map[StringTrim, LIST2, {-1}]},
     Pick[l2, Intersection[l1, #] != {} & /@ l2[[All, 2]]]]
(* same output *)

If you want the first element of a sublist that satisfies the selection criterion:

With[{l1 = Map[StringTrim, LIST1, {-1}], l2 = Map[StringTrim, LIST2, {-1}]},
 Pick[l2[[All, 1]], Intersection[l1, #] != {} & /@ l2[[All, 2]]]]
(* {"Cl fug k9"} *)

More alternatives to specify the selector array in Pick:

With[{l1 = Map[StringTrim, LIST1, {-1}], l2 = Map[StringTrim, LIST2, {-1}]},
 Pick[l2[[All, 1]], (Or @@ StringMatchQ[#, Alternatives @@ l1]) & /@ l2[[All, 2]]]]
(*  {"Cl fug k9"} *)

With[{l1 = Map[StringTrim, LIST1, {-1}], l2 = Map[StringTrim, LIST2, {-1}]},
 Pick[l2[[All, 1]], (! FreeQ[#, Alternatives @@ l1]) & /@ l2[[All, 2]]]]
(*  {"Cl fug k9"} *)