Properties of $n$-ary groups connected with the affine geometry are considered. Some conditions for an $n$-ary $rs$-group to be derived from a binary group are given. Necessary and sufficient conditions for an $n$-ary group $<\theta ,b>$-derived from an additive group of a field to be an $rs$-group are obtained. The existence of non-commutative $n$-ary $rs$-groups which are not derived from any group of arity $m<n$ for every $n\ge 3$, $r>2$ is proved.
Ultrastructural characters of spermiogenesis and mature spermatozoon of Triaenorhina rectangula (Fuhrmann, 1908) are examined by transmission electron microscopy. Spermiogenesis follows the Bâ and Marchand's Type III spermiogenesis of cestodes. The process begins with the formation of a differentiation zone containing two centrioles and a cytoplasmic protrusion. The centrioles are associated with vestigial striated roots. One of the centrioles develops a free flagellum externally to the cytoplasmic protrusion. After a slight rotation, the free flagellum fuses with the cytoplasmic protrusion. In the final stage of spermiogenesis, a single crested body appears in the anterior part of the differentiating spermatozoon. The anterior extremity of the mature spermatozoon is characterised by an apical cone and a single crested body. The axoneme is of the 9+''1'' trepaxonematan type. A periaxonemal sheath and electron-dense rods are described in some parts of the mature spermatozoon. The nucleus is electron-dense and spirally coiled around the axoneme. The cortical microtubules are spirally arranged at an angle of about 40° to the spermatozoon axis. The present results show that the ultrastructural characters of spermiogenesis and mature spermatozoon of T. rectangula resemble most closely those in taeniids and metadilepidids. The comparison of these results with the only previous spermiological description of a paruterinid species reveals differences relative to the occurrence of filamentous rods of electron-dense material versus intracytoplasmic walls in the mature spermatozoon that may reflect the polyphyletic character of the Paruterinidae.