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In my textbook, under the topic "Asymmetric and Dissymmetric Compounds", the following statement is given:
A molecule which does not possess plane of symmetry, centre of symmetry, and alternating axis of symmetry is called dissymmetric.
Why the definition didn't include the "axis of symmetry" as a condition for molecular dissymmetry?
From Wikipedia:
A chiral compound can contain no improper axis of rotation ($S_{n}$), which includes planes of symmetry and inversion center. Chiral molecules are always dissymmetric (lacking $S_{n}$) but not always asymmetric (lacking all symmetry elements except the trivial identity). Asymmetric molecules are always chiral.
That means that a dyssymetric molecule lacks of $S_{n}$ axis(planes of symmetry and inversion centers) but can have $C_{n}$ axis of rotation. For example the following molecule is dissymetric: it does not have any plane of symmetry or inversion center but it has a $C_{2}$ axis of rotation(the "axis of rotation" is a synonyms of the "axis of symmetry" you mentioned in your question).
