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The number of generators and orders of Abelian subgroups of finite \(p\)-groups. (English) Zbl 0403.20014

Translation from Mat. Zametki 23, 337–341 (1978; Zbl 0388.20018).

MSC:

20D15 Finite nilpotent groups, \(p\)-groups
20D60 Arithmetic and combinatorial problems involving abstract finite groups
20D25 Special subgroups (Frattini, Fitting, etc.)
11N45 Asymptotic results on counting functions for algebraic and topological structures

Citations:

Zbl 0388.20018
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References:

[1] Kourovsk Notebook (Unsolved Problems of Group Theory) [in Russian], 4th ed., Izd. Sib. Otd. Akad. Nauk. SSSR, Novosibirsk (1973).
[2] B. Huppert, Endliche Gruppen, I, Springer-Verlag, Berlin-New York (1967).
[3] A. R. Patterson (MacWilliams), ”The minimal number of generators for p-subgroups of GL(n, p),” J. Algebra,32, No. 1, 132–140 (1974). · Zbl 0293.20020 · doi:10.1016/0021-8693(74)90176-8
[4] Yu. I. Merzlyakov, ”On locally solvable groups of finite rank,” Algebra Logika,3, No. 2, 5–16 (1964);8, No. 6, 686–690 (1969).
[5] J. L. Alperin, ”Large Abelian subgroup of p-groups,” Trans. Am. Math. Soc.,117, No. 5, 10–20 (1965). · Zbl 0132.27204
[6] W. Burnside, ”On some properties of groups whose orders are powers of primes,” Proc. London Math. Soc. (2),11, 225–245 (1912). · JFM 43.0198.02 · doi:10.1112/plms/s2-11.1.225
[7] M. I. Kargapolov and Yu. I. Merzlyakov, Foundations of Group Theory [in Russian], Nauka, Moscow (1977). · Zbl 0499.20001
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