In the title compound, C(16)H(15)N(3)O(3), the dihedral angle between the approximately planar benzimidazolyl group (r.m.s. deviation = 0.010 Å) and the pyrrolidine ring is 78.20 (6)°. The C-C-N bond angle of the bridging CH(2) group is 112.14 (16)°. In the crystal, mol-ecules are linked via N-H⋯N hydrogen bonds, forming infinite chains parallel to [101] and [10[Formula: see text]].

‎In this paper‎, ‎we obtain the dimensions of symmetry classes of polynomials associated with‎ ‎the irreducible characters of the dihedral group as a subgroup of‎ ‎the full symmetric group‎. ‎Then we discuss the existence of o-basis‎ ‎of these classes‎.

a group g is said to be a (pf)c-group or to have polycyclic-by-finite conjugacy classes, if g/c_{g}(x^{g}) is a polycyclic-by-finite group for all xin g. this is a generalization of the familiar property of being an fc-group. de falco et al. (respectively, de giovanni and trombetti) studied groups whose proper subgroups of infinite rank have finite (respectively, polycyclic) conjugacy classes. ...

In the title zwitterion, C(15)H(13)NO(4), obtained from the condensation of 5-amino-salicylic acid and 4-meth-oxy-benz-alde-hyde, the 4-hydoxyanilinic group of the 5-amino-salicylic acid moiety and the 4-meth-oxy-benzaldehyde moiety are twisted with respect to one another, making a dihedral angle of 10.37 (7)°. The carboxyl-ate group makes a dihedral angle of 5.7 (2)° with the parent 4-hydoxyan...

We study faithful representations of the discrete Lorentz symmetry operations parity $\mathbf P$ and time reversal T$, which involve complex phases when acting on fermions. If phase is a rational multiple $\pi$ then P^{2 n}=1$ for some positive integer $n$ it shown that, this case, T$ generate group, dicyclic group (also known as generalised quaternion group) are generalisations dihedral groups...