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Let G be a group and let p be a prime number. If the setA(G) of all commuting automorphisms of G forms a subgroup of Aut(G), then G is called A(G)-group. In this paper we show that any p-group withcyclic maximal subgroup is an A(G)-group. We also find the structureof the group A(G) and we show that A(G) = Autc(G). Moreover, weprove that for any prime p and all integers n 3, there exists a non-abelian A(G)-group of order pn in which A(G) = Autc(G). If p > 2, then A(G) = Zp × Zpn−2 and if p = 2, then A(G) = Z2 × Z2 × Z2n−3 orZ2 × Z2.
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참고문헌 (7)
참고문헌 신청
D. J. S. Robinson / 1982 / Robinson, A Course in the Theory of Groups / Springer-Verlag
D. S. Dummit / 1991 / Abstract Algebra / Prentice-Hall, Inc
F. Vosooghpour / 2013 / On commuting automorphisms of p-groups / Comm. Algebra 41 (4) : 1292 ~ 1299
I. N. Herstein / 1986 / Problems and solutions: Solutions of elementary problems: E3039 / Amer. Math. Monthly 93 (10) : 816 ~ 817
M. Deaconescu / 2001 / Right 2-Engel elements and commuting automorphism of group / J. Algebra 238 (2) : 479 ~ 484
D. S. Dummit / 1991 / Abstract Algebra / Prentice-Hall, Inc
F. Vosooghpour / 2013 / On commuting automorphisms of p-groups / Comm. Algebra 41 (4) : 1292 ~ 1299
I. N. Herstein / 1986 / Problems and solutions: Solutions of elementary problems: E3039 / Amer. Math. Monthly 93 (10) : 816 ~ 817
M. Deaconescu / 2001 / Right 2-Engel elements and commuting automorphism of group / J. Algebra 238 (2) : 479 ~ 484
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