NOVELTY - A compound containing residue obtained by removing at least one hydrogen from fluorene-type compound (I), is new.    USE - New compound is used for composition for liquid composition used for thin film for element e.g. light emitting element, organic electroluminescent element and photoelectric element for display apparatus (all claimed) and solar cell.    ADVANTAGE - The compound containing residue obtained by removing at least one hydrogen from fluorene-type compound has excellent hole injection property.    DETAILED DESCRIPTION - A compound containing residue obtained by removing at least one hydrogen from fluorene-type compound of formula (I), is new.    R1=H, alkyl, aryl, arylalkyl, acyl or monovalent heterocyclyl (all optionally substituted);    R2=H, alkyl, alkoxy, aryl, aryloxy, arylalkyl, aryl alkoxy, alkenyl, aryl alkenyl, acyl, acyloxy, monovalent heterocyclyl or heterocyclyl oxy (all optionally substituted);    or two of R2+C=ring;    R4=H, alkyl, aryl, arylalkyl or monovalent heterocyclyl (all optionally substituted);    or two of R4=C;    R15=alkyl, alkoxy, aryl, aryloxy, arylalkyl, aryl alkoxy, alkenyl, aryl alkenyl, alkynyl, aryl alkynyl, amino, silyl, halo, acyl, acyloxy, carbamoyl, monovalent heterocyclyl, heterocyclyl oxy, carboxy, nitro or cyano (all optionally substituted);and    e=0-6.    INDEPENDENT CLAIMS are included for the following:    (1) compound containing piperidine-containing repeating unit of formula (IIa);    (2) manufacture of compound containing nitrogen-containing repeating unit of formula (V), which involves reacting anthracene-type compound of formula (VI) and halogenating agent;    (3) manufacture of compound containing nitrogen-containing repeating unit (V);    (4) manufacture of anthracene-type compound (VI), which involves reacting hydroxyl-containing compound of formula (VII) in presence of an acid;    (5) hydroxyl-containing compound (VII);    (6) manufacture of hydroxyl-containing compound (VII), which involves reacting carboxyl group-containing compound of formula (VIII) with reducing agent of formula: R17-M;    (7) carboxyl group-containing compound (VIII);    (8) manufacture of carboxyl group-containing compound (VIII), which involves reacting fluorene-type compound (IX) and amino group-containing compound of formula (X) in presence of transition metal catalyst and base;    (9) composition, which contains compound (I), and hole transport material, electron transport material and/or luminescent material; and    (10) element, which has electrode containing anode and cathode, and organic layer containing compound (I) provided between electrodes.    R3=R15;    a=0-5;    X1=polymerizable group;    R16=alkyl, aryl, aryl alkyl or monovalent heterocyclyl (all optionally substituted);    R17=alkyl, alkoxy, aryl, aryloxy, arylalkyl, aryl alkoxy, alkenyl, aryl alkenyl, acyl, acyloxy, monovalent heterocyclyl or heterocyclyloxy;    M=lithium or magnesium monohalide;    g=0-4;    f=0-2;and    X3=chloro, bromo or iodo.