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- W2024294525 abstract "In this note, an example is constructed which gives a negative answer to the following question posed by R. S. Pierce [2, p. 367]. Let 73 be a basic £-group, and 73 the torsion completion of 73. Let P be a subgroup of the socle of 73 such that 73 [|>]C?. Let a be an endomorphism of 73 such that a(P) C?, Does there exist a pure subgroup G of 73 such that 73CG, G[p] =P and a(G) CG? Let N be the set of positive integers and let 73= E>'e«©73,be a standard basic group with projections p Bt. Note that B{= {bi} is cyclic and of order p'. For notational convenience, let c, = ^'-1&,-. Let y= E''eAr Cn and let P be the subgroup of 73[p] generated by 73 [p] and {y}. Let a be the endomorphism of 73 determined by the conditions:" @default.
- W2024294525 created "2016-06-24" @default.
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- W2024294525 date "1966-03-01" @default.
- W2024294525 modified "2023-09-24" @default.
- W2024294525 title "A problem on endomorphisms of primary abelian groups" @default.
- W2024294525 cites W3135668875 @default.
- W2024294525 doi "https://doi.org/10.1090/s0002-9939-1966-0191960-5" @default.
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