Editing Core (group theory) (section)

===Solvable radicals===
A related subgroup in concept and notation is the solvable radical.  The '''solvable radical''' is defined to be the largest [[solvable group|solvable]] normal subgroup, and is denoted <math>O_\infty(G)</math>.  There is some variance in the literature in defining the ''p''′-core of ''G''.  A few authors in only a few papers (for instance [[John G. Thompson]]'s N-group papers, but not his later work) define the ''p''′-core of an insoluble group ''G'' as the ''p''′-core of its solvable radical in order to better mimic properties of the 2′-core.