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?

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    $\begingroup$ Because axes of symmetry are irrelevant for the question at hand. $\endgroup$ – Ivan Neretin Aug 8 '19 at 12:18
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    $\begingroup$ chemistry.stackexchange.com/questions/104409/… $\endgroup$ – Ivan Neretin Aug 8 '19 at 12:48
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    $\begingroup$ For the record, over a 10-year career in chemistry, I have never heard anyone use the word "dissymmetric." The proper word is "chiral." $\endgroup$ – Zhe Aug 8 '19 at 13:38
  • $\begingroup$ @Zhe, Thank you for your reply. Actually, it is given in my textbook like that. I am also used to the term chiral, but not dissymmetric. $\endgroup$ – Guru Vishnu Aug 8 '19 at 13:42

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).

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