A structure theorem is proved for finite groups with the property that, for some integer m with m ≥ 2, every proper quotient group can be generated by m elements but the group itself cannot.
Dalla Volta, F., Lucchini, A. (1998). Finite groups that need more generators than any proper quotient. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 64(1), 82-91 [10.1017/s1446788700001312].
Finite groups that need more generators than any proper quotient
Dalla Volta, F;
1998
Abstract
A structure theorem is proved for finite groups with the property that, for some integer m with m ≥ 2, every proper quotient group can be generated by m elements but the group itself cannot.
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