In general, element splitting operation on a matroid M with ground set E is the operation defined by creating a single element coextension of M by adding an element x that creates a cocircuit with T ⊂ E which is not a cocircuit of M . And then deletion of x from this coextension gives a T -split of M denoted by MT . Note that T -split of M may not preserve the n-connectivity of the matroid M . The present paper defines related notion of element splitting operation for matroids representable over GF (p) which preserves the n-connectivity of the matroid and characterizes circuits, bases and hyperplanes of the resulting matroid. The effect of this operation on Eulerian, bipartite and connected matroids which are representable over GF (p) is also studied.

We extend the splitting operation from binary matroids (Raghunathan et al., 1998) to p -matroids, where p -matroids refer to matroids representable over GF (p). We also characterize circuits, bases, and independent sets of the resulting matroid. Sufficient conditions to yield Eulerian p -matroids from Eulerian and non-Eulerian p -matroids by applying the splitting operation are obtained. A class of connected p -matroids that gives connected p -matroids under the splitting operation is characterized.

The es -splitting operation on binary bridge-less matroids never produces an Eulerian matroid. But for matroids representable over GF (p), (p > 2), called p -matroids, the essplitting operation may yield Eulerian matroids. In this work, we introduce es -splitting operation for p -matroids and characterize a class of p -matroids yielding Eulerian matroids after the es -splitting operation. Characterization of circuits, and bases of the resulting matroid, after the es -splitting operation, in terms of circuits, and bases of the original matroid, respectively, are discussed. We also proved that the es -splitting operation on p -matroids preserves connectivity and 3-connectedness. Sufficient condition to obtain Hamiltonian pmatroid from Hamiltonian p -matroid under es -splitting operation is also provided.