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We study more extensively and completely for global gauge anomalies with somesemisimple gauge groups as initiated in ref.1. A detailed and complete proof orderivation is provided for the Z_2 global gauge anomaly given in ref.1 for agauge theory with the semisimple gauge group SU(2)\times SU(2)\times SU(2) inD=4 dimensions and Weyl fermions in the irreducible representation (IR)\omega=(2,2,2) with 2 denoting the corresponding dimensions. This Z_2 anomalywas used in the discussions related to generic SO(10) and supersymmetric SO(10)unification theories^1 for the total generation numbers of fermions and mirrorfermions. Our result^1 that the global anomaly coefficient formula is given byA(\omega)=exp[i{\pi}Q_2(\Box)]=-1 in this case with Q_2(\Box) being the Dynkinindex for SU(8) in the fundamental IR (\Box)=(8) is also discussed, and asshown by our results^1 that the semisimple gauge transformations collectivelymay have physical consequences which do not correspond to successive simplegauge transformations. The similar result given in ref.1 for the Z_2 globalgauge anomaly of gauge group SU(2)\times SU(2) is also discussed. We also givea complete proof for some relevent topological results. Gauge anomalies for therelevant semisimple gauge groups are also briefly discussed in higherdimensions, especially for self-contragredient representations, withdiscussions involving trace identities relating to ref.14. We also remark theconnection of our results and discussions to the total generation numbers inrelevant theories.Comment: 23 page

SOME GLOBAL ASPECTS OF GAUGE ANOMALIES OF SEMISIMPLE GAUGE GROUPS AND FERMION GENERATIONS IN GUT AND SUPERSTRING THEORIES