We consider a natural generalization of the concept order an element in group [Formula: see text]: text] is said to have subgroup (respectively, coset text]) if first strictly positive integer such that text]). study this notion and its algorithmic properties realm free groups some related families. Both negative (algorithmic) results emerge setting. On side, among other results, we prove eleme...

Abstract In this manuscript we will present the theoretical framework of recently proposed infinite derivative theory gravity with a non-symmetric connection. We explicitly derive field equations at linear level and obtain new solutions non-trivial form torsion tensor in presence fermionic source, show that these are both ghost singularity-free.