In this paper we define a new sub class of Petri nets called algebraic conservative Petri nets (ACPN) for a given symmetric group S_n . We prove that the resulting Petri net (ACPN) is a marked graph . In particular, we show that the algebraic conservative Petri nets associated with S₃ and S₅ has decompositions ={_1,2,3,4,5 }and ={_{1,2,3,4, . . . ,84}} respectively, for the  sets of places such that each block _i is both siphon and trap and hence the underlying directed graphs of these algebraic conservative Petri nets are Eulerian. Also we show that each of theACPN associated with these groups has a subset of places which are both siphon and trap such that the input transitions equal the output transitions and both of them equal to the set of all transitions of these algebraic conservative Petri nets and hence that the underlying directed graphs of these algebraic conservative Petri nets associated with S₃ and S₅ are Hamiltonian.

Key words: Algebraic conservative Petri nets, siphons, traps, symmetric groups , directed graphs