Groups with normalizer condition

1972 ◽  
Vol 198 (4) ◽  
pp. 179-187 ◽  
Author(s):  
Hermann Heineken ◽  
Ismail J. Mohamed
Keyword(s):  
Normalizer Condition

Finite groups with primary normalizer condition

1981 ◽  
Vol 21 (3) ◽  
pp. 398-403
Author(s):  
V. A. Kreknin ◽  
V. V. Tsybulenko
Keyword(s):  
Finite Groups ◽  
Normalizer Condition

A note on the normalizer condition

1973 ◽  
Vol 74 (1) ◽  
pp. 11-15 ◽  
Author(s):  
B. Hartley
Keyword(s):  
Wreath Product ◽  
Normalizer Condition ◽  
Trivial Group ◽  
Trivial Centre

The first example of a non-trivial group satisfying the normalizer condition but having trivial centre was obtained by Heineken and Mohamed (1). In fact, the group they constructed satisfies the stronger condition that all its proper subgroups are subnormal and nilpotent. In this note we use a construction suggested by their approach to obtain such a group G as a subgroup of the restricted wreath product Cp ≀ Cp∞. The fact that G is given as a subgroup of a well known group makes it rather easier to investigate its properties, and in particular to see that its centre Z(G) is trivial.

Finite groups with a normalizer condition

1981 ◽  
Vol 21 (6) ◽  
pp. 857-860
Author(s):  
L. I. Shidov
Keyword(s):  
Finite Groups ◽  
Normalizer Condition

scholarly journals A group with trivial centre satisfying the normalizer condition

1968 ◽  
Vol 10 (3) ◽  
pp. 368-376 ◽  
Author(s):  
H Heineken ◽  
I.J Mohamed
Keyword(s):  
Normalizer Condition ◽  
Trivial Centre
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