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group

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group


  4  definitions  found 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
  Group  \Group\,  n.  [F  groupe,  It  gruppo  groppo,  cluster,  bunch, 
  packet,  group  of  G.  origin:  cf  G.  krepf  craw,  crop,  tumor, 
  bunch.  See  {Crop},  n.] 
  1.  A  cluster,  crowd,  or  throng;  an  assemblage,  either  of 
  persons  or  things  collected  without  any  regular  form  or 
  arrangement;  as  a  group  of  men  or  of  trees;  a  group  of 
  isles. 
 
  2.  An  assemblage  of  objects  in  a  certain  order  or  relation, 
  or  having  some  resemblance  or  common  characteristic;  as 
  groups  of  strata. 
 
  3.  (Biol.)  A  variously  limited  assemblage  of  animals  or 
  plants,  having  some  resemblance,  or  common  characteristics 
  in  form  or  structure.  The  term  has  different  uses,  and  may 
  be  made  to  include  certain  species  of  a  genus,  or  a  whole 
  genus,  or  certain  genera,  or  even  several  orders 
 
  4.  (Mus.)  A  number  of  eighth  sixteenth,  etc.,  notes  joined 
  at  the  stems;  --  sometimes  rather  indefinitely  applied  to 
  any  ornament  made  up  of  a  few  short  notes. 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
  Group  \Group\,  v.  t.  [imp.  &  p.  p.  {Grouped};  p.  pr  &  vb  n. 
  {Grouping}.]  [Cf.  F.  grouper.  See  {Group},  n.] 
  To  form  a  group  of  to  arrange  or  combine  in  a  group  or  in 
  groups,  often  with  reference  to  mutual  relation  and  the  best 
  effect;  to  form  an  assemblage  of 
 
  The  difficulty  lies  in  drawing  and  disposing,  or  as 
  the  painters  term  it  in  grouping  such  a  multitude  of 
  different  objects.  --Prior. 
 
  {Grouped  columns}  (Arch.),  three  or  more  columns  placed  upon 
  the  same  pedestal. 
 
  From  WordNet  r  1.6  [wn]: 
 
  group 
  adj  :  for  or  by  a  group  rather  than  individuals;  "dipping  each  his 
  bread  into  a  communal  dish  of  stew"-  Paul  Roche;  "a 
  communal  settlement  in  which  all  earnings  and  food  were 
  shared";  "a  group  effort"  [syn:  {communal},  {group(a)}] 
  n  1:  any  number  of  entities  (members)  considered  as  a  unit  [syn: 
  {grouping}] 
  2:  two  or  more  atoms  bound  together  as  a  single  unit  and 
  forming  part  of  a  molecule  [syn:  {radical}] 
  3:  a  set  that  is  closed,  associative,  has  an  identity  element 
  and  every  element  has  an  inverse  [syn:  {mathematical  group}] 
  v  1:  arrange  into  a  group  or  groups;  "Can  you  group  these  shapes 
  together?" 
  2:  form  a  group  or  group  together  [syn:  {aggroup}] 
 
  From  The  Free  On-line  Dictionary  of  Computing  (13  Mar  01)  [foldoc]: 
 
  group 
 
  A  group  G  is  a  non-empty  {set}  upon  which  a  {binary}  operator 
  *  is  defined  with  the  following  properties  for  all  a,b,c  in  G: 
 
  Closure:  G  is  closed  under  *,  a*b  in  G 
  Associative:  *  is  associative  on  G,  (a*b)*c  =  a*(b*c) 
  Identity:  There  is  an  identity  element  e  such  that 
  a*e  =  e*a  =  a. 
  Inverse:  Every  element  has  a  unique  inverse  a'  such  that 
  a  *  a'  =  a'  *  a  =  e.  The  inverse  is  usually 
  written  with  a  superscript  -1. 
 
  (1998-10-03) 
 
 




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