ESTONIAN ACADEMY
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eesti teaduste
akadeemia kirjastus
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On endomorphisms of groups of order 32 with maximal subgroups C24 or C42 ; pp. 1–14

Full article in PDF format | doi: 10.3176/proc.2016.1.04

Authors
Piret Puusemp, Peeter Puusemp

Abstract

It is proved that each group of order 32 that has a maximal subgroup isomorphic to C2 x C2 x C2 x C2 or C4 x C4 is determined by its endomorphism semigroup in the class of all groups.


References

  1. Alperin, J. L. Groups with finitely many automorphisms. Pacific J. Math., 1962, 12, 1–5.
http://dx.doi.org/10.2140/pjm.1962.12.1

  2. Gramushnjak, T. and Puusemp, P. A characterization of a class of groups of order 32 by their endomorphism semigroups. Algebras, Groups Geom., 2005, 22(4), 387–412.

  3. 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

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

  5. 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

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

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

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

  9. Puusemp, P. Characterization of a semidirect product of groups by its endomorphism semigroup. In Proceedings of the International Conference on Semigroups, Braga, June 18–23, 1999 (Smith, P., Giraldes, E., and Martins, P., eds). World Scientific, Singapore, 2000, 161–170.
http://dx.doi.org/10.1142/9789812792310_0013

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

11. Puusemp, P. Non-Abelian groups of order 16 and their endomorphism semigroups. J. Math. Sci., 2005, 131, 6098–6111.
http://dx.doi.org/10.1007/s10958-005-0463-x

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. 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

14. Puusemp, P. and Puusemp, P. On endomorphisms of groups of order 32 with maximal subgroups C8 × C2. Proc. Estonian Acad. Sci., 2014, 63, 355–371.
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.


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