Abstract
For a positive integer n, a finite p-group G is called an ℳ n -group, if all subgroups of index p n of G are metacyclic, but there is at least one subgroup of index p n−1 that is not. A classical result in p-group theory is the classification of ℳ1-groups by Blackburn. In this paper, we give a slightly shorter and more elementary proof of this result.
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References
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Qu, H. Elementary proof of a theorem of Blackburn. Front. Math. China 5, 117–122 (2010). https://doi.org/10.1007/s11464-009-0051-3
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DOI: https://doi.org/10.1007/s11464-009-0051-3