Abstract:
The main purpose of this paper is to find Artin's characters table of the group Q2m×D4 when m is an odd number, which is denoted by Ar(Q2m×D4), where Q2m is denoted to quaternion group of order 4m, such that for each positive integer m, there are two generators x and y for Q2m satisfies Q2m={xh yk, 0=h=2m-1, k=0,1}which has the properties x2m=y4=I, yxry-1=x-r and D4 is the dihedral group of order 8 is generate by a rotation r of order 4 and reflection s of order 2. The eight elements of D4 can be written as: {I*,r,r2, r3,s, sr, sr2,sr3}with properties srks = r-k, k = 0,1,2,3.
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