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- W2156489116 abstract "If a metacyclic group G of exponent p e contains a normal cyclic subgroup A of order p e and, in the case p = 2, has no nonabelian sections of order 8, then there exists in G a cyclic subgroup B such that G = AB and A ∩ B = {1}. Some consequences of the stated result are also proved. For example, if a metacyclic group of exponent p e is noncyclic and has no nonabelian sections of order 8 and A < G is cyclic of order p e , then there is a cyclic B < G such that G = AB and A ∩ B = {1}. Next, it is proved that if G > {1} is a metacyclic p-group, then exp (Φ(G)) < exp (G)." @default.
- W2156489116 created "2016-06-24" @default.
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- W2156489116 date "2013-10-31" @default.
- W2156489116 modified "2023-10-16" @default.
- W2156489116 title "ON FINITE METACYCLIC p-GROUPS" @default.
- W2156489116 cites W2106138043 @default.
- W2156489116 doi "https://doi.org/10.1142/s0219498813501028" @default.
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