Product of Polycyclic-By-Finite Groups (PPFG)

  • Behnam Razzaghmaneshi Computer science Islamic Azad University Talesh Branch
Keywords: Polycyclic-by-Finite, Soluble Group, Maximal Condition, finite group AMS classification: 2oF32

Abstract

In this paper we show that If the soluble-by-finite group G=AB is the product of two polycyclic-by-finite subgroups A and B, then G is polycyclic-by-finite

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Author Biography

Behnam Razzaghmaneshi, Computer science Islamic Azad University Talesh Branch

Assistant professor Department of Mathematics and Computer science Islamic Azad University Talesh Branch,
Talesh, Iran.

References

Amberg, B. (1973). Factorizations of Infinite Groups. Habilitationsschrift, Universität Mainz.

Amberg, B. (1980). Lokal endlich-auflösbare Produkte von zwei hyperzentralen Gruppen. Arch. Math. (Basel) 35, 228-238.

Ambrg, B., Franciosi, S., and de Giovanni, F.(1991). Rank formulae for factorized groups. Ukrain. Mat. Z. 43, 1078-1084.

Amberg, B.,Franciosi, S. ,and de Gioranni, F.(1992). Products of Groups. Oxford University Press Inc., New York.

Chernikov, N.S. (1980 c). Factorizations of locally finite groups. Sibir. Mat. Z. 21, 186-195. (Siber. Math. J. 21, 890-897.)

Amberg, B. (1985b). On groups which are the product of two abelian subgroups. Glasgow Math. J. 26, 151-156.

Itô, N. (1955).Über das Produkt von zwei abelschen Gruppen. Math.Z. 62, 400-401.

Kegel, O.H. (1961). Produkte nilpotenter Gruppen. Arch. Math. (Basel) 12, 90-93.

Robinson, D.J.S. (1986). Soluble products of nilpotent groups. J. Algebra 98, 183-196.

Wielandt, H. (1958b). Über Produkte von nilpotenten Gruppen. Illinois J. Math. 2, 611-618.

Zaitsev, D.I. (1981a). Factorizations of polycyclic groups. Mat. Zametki 29, 481-490. (Math. Notes 29, 247-252).

Lennox, J. C., and Roseblade, J.E. (1980). Soluble products of polycyclic groups. Math. Z. 170, 153-154.

Roseblade, J.E. (1965). On groups in which every subgroup is subnormal. J. Algebra 2, 402-412.

Kovacs, L. G. (1968). On finite soluble groups. Math. Z. 103, 37-39.

Robinson, D.J.S. (1972). Finiteness Conditions and Generalized Soluble Groups. Springer, Berlin.

Kegel, O. H., and Wehrfritz, B.A.F. (1973). Locally Finite Groups. North-Holland, Amsterdam.

Jetegaonker, A. V. (1974). Integral group rings of polycyclic-by-finite groups. J. Pure Appl. Algebra 4, 337-343.

Zaitsev, D.I. (1984). Soluble factorized groups. In Structure of Groups and Subgroup Characterizations, pp. 15-33. Akad. Nauk Ukrain. Inst. Mat. Kiev (9 in Russian).

Sesekin, N.F. (1968). Product of finitely connected abelian groups. Sib. Mat. Z. 9, 1427-1430. (Sib. Math. J. 9, 1070-1072.)

Sesekin, N.F. (1973). On the product of two finitely generated abelian groups. Mat. Zametki 13, 443-446. (Math. Notes 13, 266-268)

Cohn, P.M. (1956). A remark on the general product of two infinite cyclic groups. Arch. Math. (Basel) 7, 94-99.

Redei, L.(1950). Zur Theorie der faktorisierbaren Gruppen I. Acta Math. Hungar. 1, 74-98.

Szep, J. (1950). On factorisable, not simple groups. Acta Univ. Szeged Sect. Sci. Math. 13, 239-241.

Zappa, G. (1940). Sulla costruzione dei gruppi prodotto di due dati sottogruppi permutabili tra loro. In Atti del Secondo Congresso dell'Unione Matematica Italiana, pp. 119-125. Cremonese, Rome.

Neumann, B.H. (1954). Groups covered by permutable subsets. J.London Math. Soc. 29, 236-248.

Marconi, R. (1987). Sui prodotti di gruppi abeliani. Tesi di dottorato, Padova.

Heineken, H., and Lennox, J.C. (1983). A note on products of abelian groups. Arch. Math. (Basel) 41,498-501.

Zatisev, D.I. (1980). Products of abelian groups. Algebra i Logika 19, 150-172. (Algebra and Logic 19, 94-106.)

Huppert, B. (1967). Endliche Gruppen I. Springer, Berlin.

Kagel, O.H.(1965a). Zur Struktur mehrfach faktorisierter endlicher Grouppen. Math. Z. 87, 42-48.

Kegel, O.H., (1965b). on the solvability of some factorized liner groups. Illinois J.Math. 9, 535-547.

Franciosi, S., and de Giovanni, F. (1990a). On products of locally polycyclic groups. Arch. Math. (Basel) 55, 417-421.

Franciosi, S., and de Giovanni, F. (1990b). On normal subgroups of factorized groups. Ricerche Mat. 39, 159-167.

Franciosi, S., and de Giovanni, F. (1992). On trifactorized soluble of finite rank. Geom. Dedicata 38, 331-341.

Franciosi, S., and de Giovanni, F. (1992). On the Hirsch-Plotkin radical of a factorized group. Glasgow Math. J. To appear.

Franciosi, S., de Giovanni, F., Heineken, H., and Newell, M.L. (1991). On the Fitting length of a soluble product of nilpotent groups. Arch. Math. (Basel) 57, 313-318.

Sysak, Y.P. (1982). Products of infinite groups. Preprint 82.53, Akad. Nauk Ukrain. Inst. Mat. Kiev (in Russian).

Sysak, Y.P.(1986). Products of locally cyclic torsion-free groups. Algebra i Logika 25, 672-686. (Algebra and Logic 25, 425-433.)

Sysak, Y.P.(1988). On products of almost abelian groups. In Researches on Groups with Restrictions on Subgroups, pp. 81-85. Akad . Nauk Ukrain. Inst. Mat. Kiev (in Russian).

Sysak, Y.P. (1989). Radical modules over groups of finite rank. Preprint 89.18, Akad. Nauk Ukrain. Inst. Mat., Kiev (in Russian).

Wilson, J.S. (1985). On products of soluble groups of finite rank. Comment . Math. Helv. 60, 337-353.

Tomkinson, M,J. (1986). Products of abelian subgroups. Arch. Math. (Basel) 42, 107-112

Published
2019-12-18
How to Cite
Razzaghmaneshi, B. (2019). Product of Polycyclic-By-Finite Groups (PPFG). MathLAB Journal, 4, 87-94. Retrieved from https://purkh.com/index.php/mathlab/article/view/543
Section
Research Articles