Geodesic
Factorized Groups with max, min and min-p
Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 171-178

Voir la notice de l'article provenant de la source Cambridge University Press

Let be a class of groups which is closed under the forming of subgroups, epimorphic images and extensions. It is shown that every soluble product G = AB of two -subgroups A and B, one of which satisfies max or min, is an -group (Theorem A). If X satisfies an additional requirement, then every soluble product G = AB of two -subgroups A and B, one of which is a torsion group with min-p for every prime p, is an -group (Theorem B). Corollary: Every soluble product G = AB of two π-subgroups A and B with min-p for every prime p in the set of primes π, is a π -group with min-p for every p.
DOI : 10.4153/CMB-1984-026-4
Mots-clés : 20 E 22 (also 20 F 16) 
Amberg, Bernhard. Factorized Groups with max, min and min-p. Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 171-178. doi: 10.4153/CMB-1984-026-4
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[1] 1. Amberg, B., Artinian and noetherian factorized groups, Rend. Mat. Univ. Padova 55 (1976), 105–122. Google Scholar

[2] 2. Amberg, B., Factorizations of infinite soluble groups, Rocky Mountain J. of Math. 7 (1977), 1–17. Google Scholar

3. Amberg, B., Soluble products of two locally finite groups with min-p for every prime p, Rend. Mat. Univ. Padova 69 (1982) (3), 7–17. Google Scholar

[4] 4. Cernikov, N. S., Factorizations of locally finite groups, Sibir. Mat. J. 21 (1981), 830–897. Google Scholar

[5] 5. Kegel, O. H. and Wehrfritz, B. A. F., Locally finite groups, North-Holland, Amsterdam (1973). Google Scholar

[6] 6. J. Lennox and Roseblade, J., Soluble products of polycyclic groups, Math. Z. 110 (1980), 153–154. Google Scholar

[7] 7. Robinson, D. J. S., A course in the Theory of groups, Springer, New York, Heidelberg, Berlin (1980). Google Scholar

[8] 8. Zaicev, D. I., Products of abelian groups, Algebra and Logika 19 (1980), 150–172, Algebra and Logika 19 (1980), 94–106. Google Scholar

[9] 9. Zaicev, D. I., Products ofpolycyclic groups, Mat. Zametki 29 (1981), 481–490, Math. Notes 29 (1981), 247–252. Google Scholar

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