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Arch Math , 1981
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Journal of Algebra , 1984
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J London Math Soc Second Ser , 1979
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Journal of Combinatorial Theory Series a , 1989
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Geom Dedic , 1982
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An Introduction to Enumeration Alan Camina Barry Lewis , 2011
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Discrete Mathematics
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In this note we prove two theorems which contribute towards the clas-sification of line-transitiv... more In this note we prove two theorems which contribute towards the clas-sification of line-transitive designs. A special class of such designs are the projective planes and it is this problem which the paper addresses. There two main results:-Theorem A: Let G act line-transitively on a projective plane P and let M be a minimal normal subgroup of G. Then M is either abelian or simple or the order of the plane is 3, 9, 16 or 25. Theorem B: Let G be a classical simple group which acts line-transitively on a projective plane. Then the rank of G is bounded.
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Proceedings of the American Mathematical Society , 1980
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Canadian Journal of Mathematics , 1969
A group S is said to be metacyclic if it contains a normal cyclic subgroup N such that S/N is cyc... more A group S is said to be metacyclic if it contains a normal cyclic subgroup N such that S/N is cyclic. In this note the following theorem is proved. THEOREM. Let G be a group, S a metacyclic Sylow 2-subgroup of G. If S has a cyclic normal subgroup N such that S/N is cyclic of order greater than 2, then G is soluble. Remark. We show that such a group G contains a 2-nilpotent normal subgroup of index a divisor of 6. The solubility of these groups requires the solubility of groups of odd order unavoidably. Notation. All groups considered will be finite. Let G be a group, S a subset of G, A and B subgroups of G, N a normal subgroup of G. 〈S〉: the subgroup of G generated by S. NG (S): the normalizer of S in G. CG (S): the centralizer of S in G.
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Bulletin of the London Mathematical Society , 1996
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Bulletin of the London Mathematical Society , 1986
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Archiv der Mathematik , 1977
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Archiv der Mathematik , 1977
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Proceedings of the International Conference on Algebra 2010 - Advances in Algebraic Structures , 2011
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Mathematische Zeitschrift , 1979
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Mathematische Zeitschrift , 1974
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Bookmarks Related papers Mentions View impact
Arch Math , 1981
Bookmarks Related papers Mentions View impact
Journal of Algebra , 1984
Bookmarks Related papers Mentions View impact
J London Math Soc Second Ser , 1979
Bookmarks Related papers Mentions View impact
Journal of Combinatorial Theory Series a , 1989
Bookmarks Related papers Mentions View impact
Geom Dedic , 1982
Bookmarks Related papers Mentions View impact
An Introduction to Enumeration Alan Camina Barry Lewis , 2011
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Discrete Mathematics
Bookmarks Related papers Mentions View impact
In this note we prove two theorems which contribute towards the clas-sification of line-transitiv... more In this note we prove two theorems which contribute towards the clas-sification of line-transitive designs. A special class of such designs are the projective planes and it is this problem which the paper addresses. There two main results:-Theorem A: Let G act line-transitively on a projective plane P and let M be a minimal normal subgroup of G. Then M is either abelian or simple or the order of the plane is 3, 9, 16 or 25. Theorem B: Let G be a classical simple group which acts line-transitively on a projective plane. Then the rank of G is bounded.
Bookmarks Related papers Mentions View impact
Proceedings of the American Mathematical Society , 1980
Bookmarks Related papers Mentions View impact
Canadian Journal of Mathematics , 1969
A group S is said to be metacyclic if it contains a normal cyclic subgroup N such that S/N is cyc... more A group S is said to be metacyclic if it contains a normal cyclic subgroup N such that S/N is cyclic. In this note the following theorem is proved. THEOREM. Let G be a group, S a metacyclic Sylow 2-subgroup of G. If S has a cyclic normal subgroup N such that S/N is cyclic of order greater than 2, then G is soluble. Remark. We show that such a group G contains a 2-nilpotent normal subgroup of index a divisor of 6. The solubility of these groups requires the solubility of groups of odd order unavoidably. Notation. All groups considered will be finite. Let G be a group, S a subset of G, A and B subgroups of G, N a normal subgroup of G. 〈S〉: the subgroup of G generated by S. NG (S): the normalizer of S in G. CG (S): the centralizer of S in G.
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Bulletin of the London Mathematical Society , 1996
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Bulletin of the London Mathematical Society , 1986
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Archiv der Mathematik , 1977
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Archiv der Mathematik , 1977
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Proceedings of the International Conference on Algebra 2010 - Advances in Algebraic Structures , 2011
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Bookmarks Related papers Mentions View impact
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Mathematische Zeitschrift , 1979
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Mathematische Zeitschrift , 1974
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