JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (5): 1-4.doi: 10.6040/j.issn.1671-9352.0.2023.517

• Group Theory •    

Power automorphisms of an extraspecial p-group

XU Tao1, YIN Hongran2   

  1. 1. School of Science, Hebei University of Engineering, Handan 056038, Hebei, China;
    2. Department of Mathematics, Tianjin Tianshi College, Tianjin 301700, China
  • Published:2025-05-19

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Abstract: Let G be a generalized extraspecial p-group, where p is a prime. P(G)denotes the group of all power automorphisms of G.(ⅰ)When p is odd, If the exponent of G is p, then P(G)=1. If the exponent of G is p2, then P(G)≅Zp.(ⅱ)When p=2, if G is the central product of n dihedral groups of order 8, then P(G)=1. If G is the central product of n-1 dihedral groups of order 8 and a quaternion group of order 8, then P(G)≅Z2×Z2.

Key words: power automorphism, extraspecial p-group, generator, central product

CLC Number: 

  • O152
[1] LEVI F W. The ring of endomorphisms for which every subgroup of an abelian group is invariant[J]. Journal of the Indian Mathematical Society, 1946, 10:29-31.
[2] COOPER C D H. Power automorphisms of a group[J]. Mathematische Zeitschrift, 1968, 107:335-356.
[3] MORIGI M. Power automorphisms of finite p-groups[J]. Communications in Algebra, 1999, 27(10):4853-4877.
[4] WANG Junxin, GUO Xiuyun. Finite group with its power automorphism groups having small indices[J]. Acta Mathematica Sinica, English Series, 2009, 25(7):1097-1108.
[5] WINTER D. The automorphism group of an extraspecial p-group[J]. Rocky Mountain Journal of Mathematics, 1972, 2:159-168.
[6] HUPPERT B. Zur sylowstruktur aufslöbarer gruppen[J]. Archiv Der Mathematik, 1961, 12:161-169.
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