a famous theorem of schur states that for a group $g$ finiteness of $g/z(g)$‎ ‎implies the finiteness of $g'.$ the converse of schur's theorem is an interesting problem which has been considered by some‎ ‎authors‎. ‎recently‎, ‎podoski and szegedy proved the truth of the converse of schur's theorem for capable groups‎. ‎they also established an explicit bound for the index of the center of such...

a famous theorem of schur states that for a group $g$ finiteness of $g/z(g)$‎ ‎implies the finiteness of $g'.$ the converse of schur's theorem is an interesting problem which has been considered by some‎ ‎authors‎. ‎recently‎, ‎podoski and szegedy proved the truth of the converse of schur's theorem for capable groups‎. ‎they also established an explicit bound for the index of the...

‎in our paper [a‎. ‎b‎. ‎m‎. ‎basheer and j‎. ‎moori‎, ‎on a group of the form $2^{10}{:}(u_{5}(2){:}2)$] we calculated the inertia factors‎, ‎fischer matrices and the ordinary character table of the split‎ ‎extension $ 2^{10}{:}(u_{5}(2){:}2)$ by means of clifford-fischer‎ ‎theory‎. ‎the second inertia factor group of $2^{10}{:}(u_{5}(2){:}2)$‎ ‎is a group of the form $2_{-}^{1+6}{:}((3^{1+2}{...

This paper studies the MOR cryptosystem, using the auto-morphism group of the extra-special p-group of exponent p, for an odd prime p. Similar results can be obtained for extra-special p-groups of exponent p 2 and for the even prime.