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Possible Numbers of Non-Invariant Operators of a Group. [PDF]
Proc Natl Acad Sci U S A, 1944 Miller GA.
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Subgroups Transformed According to a Group of Prime Order. [PDF]
Proc Natl Acad Sci U S A, 1943 Miller GA.
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On preferential Sylow fuzzy subgroups
Quaestiones Mathematicae, 2017In this paper, for a prime p, we propose some plausible denitions for the notion of Sylow fuzzy p-subgroup of a nite group. We derive a number of results for nite fuzzy groups using one of the proposed denitions. We also discuss some of the relationships between various proposed denitions for suitability, including the crisp case, with some examples ...
B.B. Makamba, V. Murali
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Rationality and Sylow 2-subgroups
Proceedings of the Edinburgh Mathematical Society, 2010AbstractLet G be a finite group. If G has a cyclic Sylow 2-subgroup, then G has the same number of irreducible rational-valued characters as of rational conjugacy classes. These numbers need not be the same even if G has Klein Sylow 2-subgroups and a normal 2-complement.
Navarro, Gabriel, Tent, Joan
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Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1961
Most of the well-known theorems of Sylow for finite groups and of P. Hall for finite soluble groups have been extended to certain restricted classes of infinite groups. To show the limitations of such generalizations, examples are here constructed of infinite groups subject to stringent but natural restrictions, groups in which certain Sylow or Hall ...
Kovacs, L. G. +2 more
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Most of the well-known theorems of Sylow for finite groups and of P. Hall for finite soluble groups have been extended to certain restricted classes of infinite groups. To show the limitations of such generalizations, examples are here constructed of infinite groups subject to stringent but natural restrictions, groups in which certain Sylow or Hall ...
Kovacs, L. G. +2 more
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Fuzzy Sets and Systems, 1992
The author defines fuzzy Sylow \(p\)-subgroups of a group \(G\). Some of the results are: (i) A subgroup of a finite group \(G\) is a Sylow \(p\)-subgroup iff its characteristic function is a fuzzy Sylow \(p\)-subgroup of \(G\), (ii) If \(\mu\), \(\theta\) are two fuzzy Sylow \(p\)-subgroups of \(G\) such that \(\text{Im }\mu = \text{Im }\theta\), then
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The author defines fuzzy Sylow \(p\)-subgroups of a group \(G\). Some of the results are: (i) A subgroup of a finite group \(G\) is a Sylow \(p\)-subgroup iff its characteristic function is a fuzzy Sylow \(p\)-subgroup of \(G\), (ii) If \(\mu\), \(\theta\) are two fuzzy Sylow \(p\)-subgroups of \(G\) such that \(\text{Im }\mu = \text{Im }\theta\), then
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ON SYLOW SUBGROUPS OF LINEAR GROUPS
Mathematics of the USSR-Sbornik, 1990Main result is Theorem. Let G be a p-solvable finite group which has a faithful irreducible (complex) character of degree \(n=2p-2\), where \(p\geq 3\) is a prime number. Then if a Sylow 2-subgroup of G is abelian then the Sylow p-subgroup P of G is invariant in G. - The proof is based on Theorem.
Romanovskij, A. V., Yadchenko, A. A.
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Sylow Normalizers with a Normal Sylow 2-Subgroup
Proceedings of the Edinburgh Mathematical Society, 2008AbstractIf G is a finite solvable group and p is a prime, then the normalizer of a Sylow p-subgroup has a normal Sylow 2-subgroup if and only if all non-trivial irreducible real 2-Brauer characters of G have degree divisible by p.
Gabriel Navarro, Lucía Sanus
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Groups with Metacyclic Sylow 2-Subgroups
Canadian Journal of Mathematics, 1969A 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.
Camina, A. R., Gagen, T. M.
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