1987
DOI: 10.1016/0022-4049(87)90028-4
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Group automorphisms inducing the identity map on cohomology

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Cited by 66 publications
(35 citation statements)
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“…As before, we have B = ⟨b, c⟩, where It is interesting to see that the result is not true even when the amalgamating normal subgroup is of order 8 by the following example [13]. The map ϕ : x → x, y → y, z → x 4 z defines a class-preserving automorphism of A which is not inner [7]. Similarly, the map ϕ 1 : x → x, y 1 → y 1 , z 1 → x 4 z 1 defines a class-preserving automorphism of B.…”
Section: Case 2 C ∈ Z(a) and C ̸ ∈ Z(b)mentioning
confidence: 89%
“…As before, we have B = ⟨b, c⟩, where It is interesting to see that the result is not true even when the amalgamating normal subgroup is of order 8 by the following example [13]. The map ϕ : x → x, y → y, z → x 4 z defines a class-preserving automorphism of A which is not inner [7]. Similarly, the map ϕ 1 : x → x, y 1 → y 1 , z 1 → x 4 z 1 defines a class-preserving automorphism of B.…”
Section: Case 2 C ∈ Z(a) and C ̸ ∈ Z(b)mentioning
confidence: 89%
“…If this equality holds, then we say that G has the normalizer property. This equality was proved for finite nilpotent groups by Coleman [1] and later by Jackowscki and Marciniak [5] for finite groups having a normal Sylow 2-subgroup. In particular, the normalizer property holds for finite groups of odd order.…”
Section: Introductionmentioning
confidence: 90%
“…Lemma 2.5 (Jackowscki and Marciniak [5]). Let S be a fixed Sylow 2-subgroup of a finite group G and I S ¼ fj u j u A N UðZGÞ ðGÞ; j u j S ¼ id; j 2 u ¼ idg.…”
Section: Lemma 24 (Coleman [1])mentioning
confidence: 99%
“…Coleman's contribution [1] is well known, but the first version of the lemma appears in an article of Ward [19] as a contribution to a seminar run by Richard Brauer at Harvard. See also [15, Proposition 1.14], [7,2.6 Theorem]. Actually, for its proof it is only needed that p is not invertible in the commutative ring R.…”
Section: ])mentioning
confidence: 99%