Units in the group algebra FS_3 - Gupta, Abhinay Kumar; Sharma, R. K. (Ukrains’kyi Matematychnyi Zhurnal, 2026)
UDC 512.552 We explicitly describe each unit of a group algebra Z_p S_3 for each positive prime p ≥ 5 by using a characterization of the group algebra of the metacyclic group G= x,cx^3=1, c^n=1, cxc^-1 = x^-1 over the finite field F of characteristic p, where p is a positive prime such that p mid 3n. Based on our findings, we pose a conjecture on the number of roots of some explicit polynomials over the prime field Z_p for further academic explorations.