Geodesic
A note on groups with non-central norm
Glasgow mathematical journal, Tome 36 (1994) no. 1, pp. 37-43

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The norm K(G) of a group G is the subgroup of elements of G which normalize every subgroup of G. Under the name kern this subgroup was introduced by Baer [1]. The norm is Dedekindian in the sense that all its subgroups are normal. A theorem of Dedekind [5] describes the structure of such groups completely: if not abelian they are the direct product of a quaternion group of order eight and an abelian group with no element of order four. Baer [2] proves that a 2-group with non-abelian norm is equal to its norm. 
Bryce, R. A.; Rylands, L. J. A note on groups with non-central norm. Glasgow mathematical journal, Tome 36 (1994) no. 1, pp. 37-43. doi: 10.1017/S0017089500030524
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[1] 1.Baer, R., Der Kern eine charakteristische Untergruppe. Compositio Math. 1 (1935), 254–283. Google Scholar

[2] 2.Baer, R., Gruppen mit Hamiltonschen Kern. Compositio Math. 2 (1935), 241–246. Google Scholar

[3] 3.Bryce, R., Cossey, John and Ormerod, E. A., A note on p-groups with power automorphisms. Glasgow Math. J. 34 (1992), 327–332. Google Scholar | DOI

[4] 4.Cannon, J. J., An introduction to the Group Theory Language Cayley. Computational Group Theory (Durham 1982) pp. 145–183, (Academic Press, London–New York, 1984). Google Scholar

[5] 5.Dedekind, R., Über Gruppen, deren sämmtliche Theiler Normaltheiler sind. Math. Ann. 48 (1897), 548–561. Google Scholar | DOI

[6] 6.Hall, M., The Theory of Groups.(Macmillan, New York, 1959). Google Scholar

[7] 7.Hughes, D., Research Problem No. 3, Bull. Amer. Math. Soc. 63 (1957), 209. Google Scholar

[8] 8.Levi, F. W., Groups in which the commutator operation satisfies certain algebraic conditions. J. Indian Math. Soc. 6 (1942), 87–97. Google Scholar

[9] 9.Meixner, Thomas, Power automorphisms of finite p-groups, Israel J. Math. 38 (1981), 345–360. Google Scholar | DOI

[10] 10.Schenkman, E., On the norm of a group. Illinois J. Math. 4 (1960), 150–152. Google Scholar | DOI

[11] 11.Strauss, E. G. and Szekeres, G., On a problem of D. R. Hughes. Proc. Amer. Math. Soc. 9 (1958), 157–158. Google Scholar | DOI

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