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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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On endomorphisms of groups of order 32 with maximal subgroups C8 x C2; pp. 355–371

(Full article in PDF format) doi: 10.3176/proc.2014.4.01


Authors

Piret Puusemp, Peeter Puusemp

Abstract

It is proved that each group of order 32 which has a maximal subgroup isomorphic to C8 x C2 is determined by its endomorphism semigroup in the class of all groups.

Keywords

group, semigroup, endomorphism semigroup.

References

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  2. Corner , A. L. S. Every countable reduced torsion-free ring is an endomorphism ring. Proc. London Math. Soc. , 1963 , 13 , 687–710.
http://dx.doi.org/10.1112/plms/s3-13.1.687

  3. Gramushnjak , T. and Puusemp , P. A characterization of a class of groups of order 32 by their endomorphism semigroups. Algebras , Groups , Geom. , 2005 , 22 , 387–412.

  4. Gramushnjak , T. and Puusemp , P. A characterization of a class of 2-groups by their endomorphism semigroups. In Generalized Lie Theory in Mathematics , Physics and Beyond (Silvestrov , S. , Paal , E. , Abramov , V. , and Stolin , A. , eds). Springer-Verlag , Berlin , 2009 , 151–159.
http://dx.doi.org/10.1007/978-3-540-85332-9_14

  5. Hall , M. , Jr. and Senior , J. K. The Groups of Order 2n , n £ 6. Macmillan , New York; Collier-Macmillan , London , 1964.

  6. Krylov , P. A. , Mikhalev , A. V. , and Tuganbaev , A. A. Endomorphism Rings of Abelian Groups. Kluwer Academic Publisher , Dordrecht , 2003.
http://dx.doi.org/10.1007/978-94-017-0345-1

  7. Puusemp , P. Idempotents of the endomorphism semigroups of groups. Acta Comment. Univ. Tartuensis , 1975 , 366 , 76–104 (in Russian).

  8. Puusemp , P. Endomorphism semigroups of generalized quaternion groups. Acta Comment. Univ. Tartuensis , 1976 , 390 , 84–103 (in Russian).

  9. Puusemp , P. A characterization of divisible and torsion Abelian groups by their endomorphism semigroups. Algebras , Groups , Geom. , 1999 , 16 , 183–193.

10. Puusemp , P. On endomorphism semigroups of dihedral 2-groups and alternating group A4. {\it Algebras , Groups , Geom. , 1999 , 16 , 487–500.

11. Puusemp , P. On the definability of a semidirect product of cyclic groups by its endomorphism semigroup. Algebras , Groups , Geom. , 2002 , 19 , 195–212.

12. Puusemp , P. Groups of order less than 32 and their endomorphism semigroups. J. Nonlinear Math. Phys. , 2006 , 13 , Supplement , 93–101.
http://dx.doi.org/10.2991/jnmp.2006.13.s.11

13. Puusemp , P. Semidirect products of generalized quaternion groups by a cyclic group. In Generalized Lie Theory in Mathematics , Physics and Beyond (Silvestrov , S. , Paal , E. , Abramov , V. , and Stolin , A. , eds). Springer-Verlag , Berlin , Heidelberg , 2009 , 141–149.
http://dx.doi.org/10.1007/978-3-540-85332-9_13

14. Puusemp , P. and Puusemp , P. On endomorphisms of groups of order 32 with maximal subgroups C4 ´ C2 ´ C2. Proc. Estonian Acad. Sci. , 2014 , 63 , 105–120.
http://dx.doi.org/10.3176/proc.2014.2.01

15. Robinson , D. J. S. A Course in the Theory of Groups. Springer-Verlag , New York , 1996.
http://dx.doi.org/10.1007/978-1-4419-8594-1

 
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Current Issue: Vol. 68, Issue 3, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December