On the nonexistence of groups with extra-special commutator subgroup

Miller, Michael D.

doi:10.1090/S0002-9939-1976-0401908-X

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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On the nonexistence of groups with extra-special commutator subgroup
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by Michael D. Miller PDF

Proc. Amer. Math. Soc. 56 (1976), 16-18 Request permission

Abstract:

In this paper, we extend a result of Joseph and Finkelstein and show that there is no group $G$ such that $G’$ is an extra-special $p$-group of exponent $> p$ ($p$ odd).

References

Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903

Groups whose commutator subgroup is an extra-special $p$-group

I. D. Macdonald, On cyclic commutator subgroups, J. London Math. Soc. 38 (1963), 419–422. MR 162839, DOI 10.1112/jlms/s1-38.1.419
W. R. Scott, Group theory, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0167513