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IT is well known that every group which contains at least one operator of order 2 must contain an odd number of such operators and that there is an infinite number of groups such that each of them contains exactly 2m + 1 operators of order 2, where m is an arbitrary positive integer or 0. It is also known that if exactly one half of the operators of a group are of order 2 then the order of this group must be of the form 2 (2m + 1) and it must be the dihedral or the generalized dihedral group of this order. Moreover, it has been proved that a group G of order

Groups containing a relatively large number of operators of order two