• R P Shukla

      Articles written in Proceedings – Mathematical Sciences

    • Transversals in non-discrete groups

      Ramji Lal R P Shukla

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      The concept of ‘topological right transversal’ is introduced to study right transversals in topological groups. Given any right quasigroupS with a Tychonoff topologyT, it is proved that there exists a Hausdorff topological group in whichS can be embedded algebraically and topologically as a right transversal of a subgroup (not necessarily closed). It is also proved that if a topological right transversal(S, TS,TS, o) is such thatTS =TS is a locally compact Hausdorff topology onS, thenS can be embedded as a right transversal of a closed subgroup in a Hausdorff topological group which is universal in some sense.

    • Structure of a Code Related to $Sp(4,q),q$ even

      N S Narasimha Sastry R P Shukla

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      We determine the socle and the radical series of the binary code associated with a finite regular generalized quadrangle of even order, considered as a module for the commutator of each of the orthogonal subgroups in the corresponding symplectic group.

    • On the Number of Isomorphism Classes of Transversals

      Vipul Kakkar R P Shukla

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      In this paper we prove that there does not exist a subgroup 𝐻 of a finite group 𝐺 such that the number of isomorphism classes of normalized right transversals of 𝐻 in 𝐺 is four.

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