مختصر البحث:
The main purpose of This paper is to find Artin,s character table Ar(Q2m×C5 )when m is odd number such that m= p_1^(s_1 ).p_2^(s_2 ),g.c.d(p_1 p_2)=1p_1 p_2>2 p_1 p_2 are primes numbers and s_1 s_2 are a positive integers numbers ;wher…
The main purpose of This paper is to find Artin,s character table Ar(Q2m×C5 )when m is odd number such that m= p_1^(s_1 ).p_2^(s_2 ),g.c.d(p_1 p_2)=1p_1 p_2>2 p_1 p_2 are primes numbers and s_1 s_2 are a positive integers numbers ;where Q2m is denoted to Quaternion group of order 4m, time is said to have only one dimension and space to have three dimension, the mathematical quaternion partakes of both these elements; in technical language it may be said to be "time plus space", or "space plus time" and in this sense it has, or at least involves a reference to four dimensions, and how the one of time of space the three might in the chain of symbols girdled " William Rowan Hamilton (Quoted in Robert Percival Graves "Life of sir William Rowan Hamilton" (3 vols.,1882,1885,1889)), andC5 is Cyclic group of order 5. In 1962, C.W.Curits & I.Reiner studied Representation Theory of finite groups, In 1976, I.M.Isaacs studied Charactrs Theory of finite groups, In 1982, M.S.Kirdar studied The Factor Group of the Z-Valued class function modulo the group of the Generalized Characters, In 1995, N.R.Mahmood studies The Cyclic Decomposition of the factor Group cf(Q2m,Z)/ ( G) (Q2m), In 2002, K-Sekiguchi studies Extensions and the Irreducibilies of the Induced Characters of Cyclic P-Group, In 2008, A.H.Abdul-Munem studied Artin Cokernel of The Quaternion group Q2m when m is an Odd number In 2006, A.S. Abed found the Artin characters table of dihedral group D when n is an odd number.
