| Article Details : |
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| | | Article Name : | | | The Cyclic Decomposition of the Factor Group
cf(Q2m×D5,Z) / ?(Q2m×D5)
when m = p, p?2, is prime number | | Author Name : | | | ATHEER RAZZAQ JASIM, Prof. NASER RASOOL MAHMOOD | | Publisher : | | | Bridge Center | | Article URL : |  | | | Abstract : | | | Let Q2m be the quaternion group of order 4m when m= p?2
is an odd number, and D5 be the dihedral group of order 10. let cf
(Q2m×D5,Z ) be the abelain group of Z–valued class function of the
group (Q2m×D5). The intersection of cf(Q2m×D5,Z) with the group of
generalized characters of (Q2m×D5).which is denoted by R(Q2m×D5) is a
normal subgroup of the group cf(Q2m×D5,Z) denoted by
R
(Q2m×D5), the
factor group cf(Q2m×D5,Z) /
R
(Q2m×D5) is a finite abelian group
denoted by K(Q2m×D5).the purpose of this paper to find
5 5 8
2(r 1)
n 1
2m 4
3
n 1
K(Q2p ?D5
) ? ? K(Q )?C ? C s ?1 ?C ?C
?
? ? when m
= p, p?2 is prime number | | Keywords : | | | cyclic decomposition, factor group, prime number |
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