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math.GR2026
Impartial games on two finite Groups
Ratan Lal, Muskan, Vipul Kakkar
In this paper, we study impartial achievement games and impartial avoidance games introduced by Anderson and Harary. Using the criteria of maximal subgroups, we study the game for…
math.GR2025
Determinant for automorphisms of semidirect product of groups
Ratan Lal, Alka Choudhary, Vipul Kakkar
A description of the endomorphisms of semidirect products of two groups as a group of matrices of maps is already known. Using this description, we have studied the con…
math.GR2024
Semidirect Product of Loops with Groups
Ratan Lal, Ramjash Gurjar, Vipul Kakkar
In this paper, we have studied the loops which are the semidirect products of a loop and a group. Also, the cummutant, nuclei and the center of such loops are studied.