A note on essential finite indecomposability and thickness in primary abelian groups

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Peter V. Danchev
Patrick W. Keef


We present a new characterization of essentially finitely indecomposable abelian $p$-groups. Parallel ideas are also applied to the socles of groups, especially in the case of groups that are pure-complete. These results are then used to discuss the class of thick abelian $p$-groups.

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Danchev, P. V., & Keef, P. W. (2013). A note on essential finite indecomposability and thickness in primary abelian groups. Tamkang Journal of Mathematics, 44(2), 163–170. https://doi.org/10.5556/j.tkjm.44.2013.1040


K. Benabdallah and R. Wilson, Thick groups and essentially finitely indecomposable groups, Can. J. Math. (3), 30(1978), 650--654.

D. Cutler and J. Irwin, Essentially finitely indecomposable abelian p-groups, Quaestiones Math., 9(1986), 135--148.

D. Cutler and C. Missel, The structure of C- decomposable p(omega +n)-projective abelian p-groups, Commun. Algebra, 12(1984), 301--319.

P. Danchev, Commutative group algebras of thick abelian p-groups, Indian J. Pure Appl. Math. (6), 36(2005), 319--328.

P. Danchev, Notes on essentially finitely indecomposable nonthick primary abelian groups, Commun. Algebra (4), 36 (2008), 1509--1513.

M. Dugas and J. Irwin, On thickness and decomposability of abelian p-groups, Israel J. Math. (2-3), 79(1992), 153--159.

P. Danchev and P. Keef, Nice elongations of primary abelian groups, Publ. Mat. (2), 54 (2010), 317--339.

P. Danchev and P. Keef, Nice bases and thickness in primary abelian groups, Rocky Mountain J. Math. (4), 41 (2011), 1127--1149.

L. Fuchs, Infinite Abelian Groups, volumes I and II, Acad. Press, New York and London, 1970 and 1973.

L. Fuchs, Vector spaces with valuations, J. Algebra, 35 (1975), 23--38.

J. Irwin and P. Keef, Primary abelian groups and direct sums of cyclics, J. Algebra, 159 (1993), 387--399.

P. Keef, Primary abelian groups admitting only small homomorphisms, Commun. Algebra (10), 23 (1995), 3615--3626.

P. Keef, Partially decomposable primary abelian groups and the generalized core class property, in Models, Modules and Abelian Groups, Walter de Gruyter, Berlin and New York, 2008, 289--299.

P. Keef, On subgroups of totally projective primary abelian groups and direct sums of cyclic groups, Contemp. Math.,576 (2012), 205--216.

R. Pierce, Homomorphisms of Primary Abelian Groups, in Topics in Abelian Groups, Scott Foresman and Co. (1963), 215--310.