Determination of a certain family of finite metabelian groups
HTML articles powered by AMS MathViewer
- by G. Szekeres PDF
- Trans. Amer. Math. Soc. 66 (1949), 1-43 Request permission
References
-
G. Bagnera, Annali di Matematica (3) vol. 1 (1898) pp. 137-228.
H. A. Bender, A determination of the group of order ${p^5}$, Ann. of Math. (2) vol. 29 (1928) pp. 61-72.
W. Burnside, Theory of groups of finite order, Cambridge, 1911.
- Paul Erdös, On some asymptotic formulas in the theory of partitions, Bull. Amer. Math. Soc. 52 (1946), 185–188. MR 14368, DOI 10.1090/S0002-9904-1946-08540-7 P. Hall, A contribution to the theory of groups of prime power orders, Proc. London Math. Soc. (2) vol. 36 (1932) pp. 29-95.
- P. Hall, The classification of prime-power groups, J. Reine Angew. Math. 182 (1940), 130–141. MR 3389, DOI 10.1515/crll.1940.182.130
- Nathan Jacobson, The Theory of Rings, American Mathematical Society Mathematical Surveys, Vol. II, American Mathematical Society, New York, 1943. MR 0008601
- G. A. Miller, Determination of all the groups of order $p^m$ which contain the abelian group of type $(m-2,1),\ p$ being any prime, Trans. Amer. Math. Soc. 2 (1901), no. 3, 259–272. MR 1500568, DOI 10.1090/S0002-9947-1901-1500568-X
- G. A. Miller, Determination of all the groups of order $p^m$, $p$ being any prime, which contain the abelian group of order $p^{m-1}$ and of type (1, 1, 1, ...), Bull. Amer. Math. Soc. 8 (1902), no. 9, 391–394. MR 1557917, DOI 10.1090/S0002-9904-1902-00918-X
- Herbert Rauter, Eine Erweiterung des Begriffs der Abelschen Gruppe: $p$-Abelsche Gruppen, Math. Z. 31 (1930), no. 1, 29–38 (German). MR 1545097, DOI 10.1007/BF01246396
- L. Rédei, Das “schiefe Produkt” in der Gruppentheorie mit Anwendung auf die endlichen nichtkommutativen Gruppen mit lauter kommutativen echten Untergruppen und die Ordnungszahlen, zu denen nur kommutative Gruppen gehören, Comment. Math. Helv. 20 (1947), 225–264 (German). MR 21933, DOI 10.1007/BF02568131
- G. Szekeres, On a certain class of metabelian groups, Ann. of Math. (2) 49 (1948), 43–52. MR 24433, DOI 10.2307/1969112
- H. S. Vandiver, On a $p$-adic representation of rings and Abelian groups, Ann. of Math. (2) 48 (1947), 22–28. MR 18647, DOI 10.2307/1969212 B. L. van d. Waerden, Moderne Algebra, vol. 1, Berlin, 1937. —, Moderne Algebra, vol. 2, Berlin, 1931.
- Louis Weisner, Groups in which the normaliser of every element except identity is abelian, Bull. Amer. Math. Soc. 31 (1925), no. 8, 413–416. MR 1561078, DOI 10.1090/S0002-9904-1925-04079-3
- A. Wiman, Über mit Diedergruppen verwandte $p$-Gruppen, Ark. Mat. Astr. Fys. 33A (1946), no. 6, 12 (German). MR 0018179 H. Zassenhaus, Lehrbuch der Gruppentheorie I, Hamburger mathematische Einzelschriften, vol. 21, 1937.
Additional Information
- © Copyright 1949 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 66 (1949), 1-43
- MSC: Primary 20.0X
- DOI: https://doi.org/10.1090/S0002-9947-1949-0032633-3
- MathSciNet review: 0032633