A group of exponent with derived length at least

Authors:
S. Bachmuth, H. Y. Mochizuki and K. Weston

Journal:
Proc. Amer. Math. Soc. **39** (1973), 228-234

MSC:
Primary 20-04

MathSciNet review:
0314943

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Abstract: There exists a group of exponent 4 such that the third term of its derived series, , is nontrivial. Furthermore, the third term of the derived series of is not contained in the ninth term of its lower central series.

**[1]**S. Bachmuth, H. A. Heilbronn, and H. Y. Mochizuki,*Burnside metabelian groups*, Proc. Roy. Soc. Ser. A**307**(1968), 235–250. MR**0236264****[2]**S. Bachmuth, H. Y. Mochizuki, and D. W. Walkup,*Construction of a non-solvable group of exponent 5*, Word problems: decision problems and the Burnside problem in group theory (Conf. on Decision Problems in Group Theory, Univ. California, Irvine, Calif. 1969; dedicated to Hanna Neumann), North-Holland, Amsterdam, 1973, pp. 39–66. Studies in Logic and the Foundations of Math., Vol. 71. MR**0412273****[3]**R. H. Bruck,*Engel conditions in groups and related questions*, Lecture Notes, Australian National University, Canberra, Jan. 1963.**[4]**Narain D. Gupta and Kenneth W. Weston,*On groups of exponent four*, J. Algebra**17**(1971), 59–66. MR**0268277****[5]**Narain D. Gupta, Horace Y. Mochizuki, and Kenneth W. Weston,*On groups of exponent four with generators of order two*, Bull. Austral. Math. Soc.**10**(1974), 135–142. MR**0338185****[6]**A. L. Tritter,*A module-theoretic computation related to the Burnside problem*, Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967) Pergamon, Oxford, 1970, pp. 189–198. MR**0262373****[7]**Tah-Zen Yuan, Thesis, University of Notre Dame, South Bend, Ind., 1969.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1973-0314943-4

Keywords:
Group of exponent 4,
derived length

Article copyright:
© Copyright 1973
American Mathematical Society