Determination of the Order of the Groups of Isomorphisms of the Groups of Order P4, where P. is a Prime ... |
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¹+p abstractly Burnside Cole and Glover congruences inconsistent defining relations elements of G exponents formulæ hold four operations further conditions G and G group G group of isomorphisms group of order Hence insure the independence JOURNAL OF MATHEMATICS Let P Q R Let x=x'p MARRIOTT mod p² morphisms N=p³ non-abelian group number of elements number of solutions O. E. Glenn operation of G operations of order order p¹ P Q R S P² Q P² Q¹ R² P² R² p³q Pkx+2xy PoQo PQ=QP Pr² Q to Qo Q-¹PQ=P Qky Rkz Qo¹Po QR=RQ R-¹PR=P R-¹QR=Q R¹PR=PoQo R¹Q R¹Qo Ro=Qo relation P Q R S RP=PR RQ=QR satisfy Section 15 set of congruences simply isomorphic single operation sponds sufficient to insure Theory of Groups transformation formulæ University of Pennsylvania W₁ W₂ x#0 mod x₂ x2 y₁ xy₁ y₁0 mod Y₂ Z₂