Registration of Trade Union:-
Any seven or more members complying with the provisions of this Act with respect to registration, apply for registration of the Trade Union under this Act.
Objective to form Trade Union:- As per Section 2 (g) & (h)
(g) "trade dispute" means any dispute between employers and workmen or between workmen and workmen, or between employers and employers which is connected with the employment or non-employment, or the terms of employment or the conditions of labour, of any person, and "workmen" means all persons employed in trade or industry whether or not in the employment of the employer with whom the trade dispute arises; and
(h) "Trade Union" means any combination, whether temporary or permanent, formed primarily for the purpose of regulating the relations between workmen and employers or between workmen and workmen, or between employers and employers, or for imposing restrictive conditions on the conduct of any trade or business, and includes any federation of two or more Trade Unions:
If your requirement is as per the above a "Trade Union" can be formed or otherwise no.