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Grinshpon, Samuil Yakovlevich

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Total publications: 30
Scientific articles: 28

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Professor
Doctor of physico-mathematical sciences (2001)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
Birth date: 05.12.1947
E-mail: ,
Keywords: Abelian groups; fully invariant subgroups; characteristic subgroups; endomorphism rings; automorphism groups; homomorphism groups; lattices of subgroups; fully invariant submodules; invariant submodules.

Subject:

Necessary and sufficient conditions under which isomorphism of endomorphism groups of abelian p-groups A and B implies isomorphism of the groups A and B have been obtained. This yields a solution of L. Fuchs's problem 41 from his monograph "Abelian groups", Budapest, 1966. The question when the group Hom(A,C) is zero is completely solved for the case when at least one of the abelian groups A, C is a torsion group. The question when the homomorphism group Hom(A,C) is zero was studied in the case when C is a homogeneous separable group. New classes of fully transitive abelian groups for which fully invariant subgroups and their lattices are described have been discovered. This makes it possible to obtain results for known classes as corollaries. Fully invariant subgroups and their lattices are completely described for separable p-groups, separable torsion free groups, vector groups and mixed completely decomposable groups. Abelian groups from different classes in which the lattice of fully invariant subgroups is distributive or generally distributive are described. We studied f.i.-correct groups, i.e. groups for which an analog of the well-known set-theoretical Cantor-Schroder-Bernstein theorem is valid. (An abelian group A is said to be f.i.-correct if for any group B isomorphism of the group A and B follows from the fact that each of the group A, B is isomorphic to a fully invariant subgroup of the other group). f.i.-correct groups are completely described for different classes of torsion groups, torsion free groups amd mixed groups. Abelian p-groups with elements of infinite height have been studied. A wide class of such groups that yields a negative solution of I. Kaplansky's problem 25 from "Problems on Abelian groups", Proceedings of the Symposium of abelian groups, New Mexico, 1963, p. 365–368 is presented.

Biography

Graduated from Faculty of Mathematics and Mechanics of Tomsk State University (TSU) in 1970 (department of algebra). Ph.D. thesis was defended in 1985. D.Sci. thesis was defended in 2000. A list of my works contains more than 80 titles.

In 1997 I was awarded the prize of the Administration of Tomsk region for high achievements in education and science.

   
Main publications:
  • Grinshpon S. Ya. Primarnye abelevy gruppy s izomorfnymi gruppami endomorfizmov // Matem. zametki. 1973. T. 14, # 5. S. 733–741.
  • Grinshpon S. Ya. O ravenstve nulyu gruppy gomomorfizmov abelevykh grupp // Izv. vuzov. Matematika. 1998. # 9. S. 42–46.
  • Grinshpon S. Ya. Vpolne kharakteristicheskie podgruppy separabelnykh abelevykh grupp // Fundament. i prikl. matem. 1998. T. 4, vyp. 4. S. 1281–1307.
  • Grinshpon S. Ya. f.i.-korrektnye abelevy gruppy // Uspekhi matem. nauk. 1999. T. 54, # 6. S. 155–156.
  • Grinshpon S. Ya. Vpolne kharakteristicheskie podgruppy abelevykh grupp bez krucheniya i ikh reshetki // Fundament. i prikl. matem. 2000. T. 6, vyp. 3. S. 747–759.

http://www.mathnet.ru/eng/person9093
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/283030

Publications in Math-Net.Ru
2019
1. S. Ya. Grinshpon, M. M. Nikolskaya, “Abelian groups isomorphic to a proper fully invariant subgroup”, Fundam. Prikl. Mat., 22:5 (2019),  29–53  mathnet
2015
2. S. Ya. Grinshpon, I. E. Grinshpon, “Normal determinability of torsion-free Abelian groups by their holomorphs”, Fundam. Prikl. Mat., 20:5 (2015),  39–55  mathnet  mathscinet; J. Math. Sci., 230:3 (2018), 377–388
3. S. Ya. Grinshpon, S. L. Fukson, “Orthogonalities in the multiplicative group $\mathbb{Q}_+$”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2015, 6(38),  18–26  mathnet  elib
2014
4. S. Ya. Grinshpon, A. K. Mordovskoi, “Correctness of Abelian torsion-free groups and determinability of Abelian groups by their subgroups”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2014, 5(31),  16–29  mathnet
2013
5. S. Y. Grinshpon, M. I. Rogozinsky, “k-full transitivity of homogeneously decomposable groups”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2013, 4(24),  5–14  mathnet
6. S. Ya. Grinshpon, I. E. Grinshpon, “Torsion free abelian groups normally determined by their holomorphs”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2013, 3(23),  23–33  mathnet
2012
7. S. Ya. Grinshpon, M. M. Nikolskaya, “Torsion IF-groups”, Fundam. Prikl. Mat., 17:8 (2012),  47–58  mathnet; J. Math. Sci., 197:5 (2014), 614–622  scopus
8. S. Ya. Grinshpon, I. E. Grinshpon, “Determinateness of torsion-free Abelian groups by their holomorphs and almost holomorphic isomorphism”, Fundam. Prikl. Mat., 17:8 (2012),  35–46  mathnet; J. Math. Sci., 197:5 (2014), 605–613  scopus
9. S. Ya. Grinshpon, “On a problem related to homomorphism groups in the theory of Abelian groups”, Fundam. Prikl. Mat., 17:8 (2012),  31–34  mathnet; J. Math. Sci., 197:5 (2014), 602–604  scopus
10. S. Y. Grinshpon, M. M. Nikolskaya, “Proper fully invariant subgroups of torsion free groups isomorphic to the group”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2012, 1(17),  11–15  mathnet
2011
11. S. Ya. Grinshpon, M. M. Nikolskaya, “Primary $IF$-groups”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2011, 3(15),  25–31  mathnet
2010
12. S. Ya. Grinshpon, M. M. Nikol'skaya (Savinkova), “$IF$-groups”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2010, 1(9),  5–14  mathnet  elib
2009
13. S. Ya. Grinshpon, T. A. Yeltsova, “Connection of divisible and reduced groups with homomorphic stability”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2009, 2(6),  14–19  mathnet
2008
14. S. Ya. Grinshpon, T. A. Yeltsova, “Homomorphic images of Abelian groups”, Fundam. Prikl. Mat., 14:5 (2008),  67–76  mathnet  mathscinet; J. Math. Sci., 163:6 (2009), 670–676  scopus
15. S. Ya. Grinshpon, I. V. Gerdt, “Abelian groups that are small with respect to different classes of groups”, Fundam. Prikl. Mat., 14:5 (2008),  55–65  mathnet  mathscinet; J. Math. Sci., 163:6 (2009), 662–669  scopus
16. S. Ya. Grinshpon, T. A. Yeltsova, “Homomorphic Stability of Direct Product Torsion Free Abelian Groups”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2008, 1(2),  32–36  mathnet
2007
17. S. Ya. Grinshpon, T. A. Yeltsova, “Homomorphic images of Abelian groups”, Fundam. Prikl. Mat., 13:3 (2007),  17–24  mathnet  mathscinet  zmath; J. Math. Sci., 154:3 (2008), 290–294  scopus
2004
18. S. Ya. Grinshpon, “Completely characteristic subgroups of completely decomposable abelian groups”, Izv. Vyssh. Uchebn. Zaved. Mat., 2004, 9,  18–23  mathnet  mathscinet; Russian Math. (Iz. VUZ), 48:9 (2004), 15–20
2003
19. S. Ya. Grinshpon, A. K. Mordovskoi, “Almost isomorphism of Abelian groups and determinability of Abelian groups by their subgroups”, Fundam. Prikl. Mat., 9:3 (2003),  21–36  mathnet  mathscinet  zmath  elib; J. Math. Sci., 135:5 (2006), 3281–3291  scopus
2002
20. S. Ya. Grinshpon, “Fully invariant subgroups of Abelian groups and full transitivity”, Fundam. Prikl. Mat., 8:2 (2002),  407–473  mathnet  mathscinet  zmath
2000
21. S. Ya. Grinshpon, “Fully invariant subgroups of torsion free Abelian groups and their lattices”, Fundam. Prikl. Mat., 6:3 (2000),  739–751  mathnet  mathscinet  zmath
1999
22. S. Ya. Grinshpon, “FI-defined Abelian groups”, Uspekhi Mat. Nauk, 54:6(330) (1999),  155–156  mathnet  mathscinet  zmath; Russian Math. Surveys, 54:6 (1999), 1240–1241  isi  scopus
1998
23. S. Ya. Grinshpon, “Fully invariant subgroups of separable Abelian groups”, Fundam. Prikl. Mat., 4:4 (1998),  1279–1305  mathnet  mathscinet  zmath
24. S. Ya. Grinshpon, “On the equality to zero of the homomorphism group of abelian groups”, Izv. Vyssh. Uchebn. Zaved. Mat., 1998, 9,  42–46  mathnet  mathscinet  zmath  elib; Russian Math. (Iz. VUZ), 42:9 (1998), 39–43
1997
25. S. Ya. Grinshpon, “Fully transitive homogeneously separable Abelian groups”, Mat. Zametki, 62:3 (1997),  471–474  mathnet  mathscinet  zmath; Math. Notes, 62:3 (1997), 393–395  isi
1995
26. S. Ya. Grinshpon, A. M. Sebel'din, “Determinability of periodic Abelian groups by their endomorphism groups”, Mat. Zametki, 57:5 (1995),  663–669  mathnet  mathscinet  zmath; Math. Notes, 57:5 (1995), 457–462  isi
1976
27. S. Ya. Grinshpon, “Some classes of primary abelian groups that are almost isomorphic with respect to fully characteristic subgroups”, Izv. Vyssh. Uchebn. Zaved. Mat., 1976, 2,  23–30  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 20:2 (1976), 20–22
1973
28. S. Ya. Grinshpon, “Primary Abelian groups with isomorphic endomorphism groups”, Mat. Zametki, 14:5 (1973),  733–740  mathnet  mathscinet; Math. Notes, 14:5 (1973), 979–982

2013
29. S. Ya. Grinshpon, A. R. Chekhlov, “P. A. Krylov. To the 65$^{\mathrm{th}}$ anniversary”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2013, 1(21),  116–122  mathnet
2011
30. S. Ya. Grinshpon, P. A. Krylov, “Заметки об истории кафедры алгебры Томского государственного университета”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2011, 3(15),  127–138  mathnet

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