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Minimal nonmodular finite p-groups

Zvonimir Janko

Sažetak

We describe first the structure of finite minimal nonmodular 2-groups G. We show that in case |G| > 25, each proper subgroup of G is Q8-free and G/(G) is minimal nonabelian of order 24 or 25. If |G/(G)| = 24, then the structure of G is determined up to isomorphism (Propositions 2.4 and 2.5). If |G/(G)| = 25, then (G) E8 and G/(G) is metacyclic (Theorem 2.8).

Then we classify finite minimal nonmodular p-groups G with p > 2 and |G| > p4 (Theorems 3.5 and 3.7). We show that G/(G) is nonabelian of order p3 and exponent p and (G) is metacyclic. Also, G/(G) Ep and G/(G) is metacyclic.

Ključne riječi

p-group; modular group; nonmodular group; quaternion group; minimal nonabelian group

Hrčak ID:

1245

URI

https://hrcak.srce.hr/1245

Datum izdavanja:

29.11.2004.

Posjeta: 1.131 *