On finite C-tidy groups

Document Type: Research Paper

Author

North-Eastern Hill University

Abstract

A group $G$ is said to be a C-tidy group if for every element $x \in G \setminus K(G)$‎, ‎the set $Cyc(x)=\lbrace y \in G \mid \langle x‎, ‎y \rangle \; {\rm is \; cyclic} \rbrace$ is a cyclic subgroup of $G$‎, ‎where $K(G)=\underset{x \in G}\bigcap Cyc(x)$‎. ‎In this short note we determine the structure of finite C-tidy groups‎.

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A. Abdollahi and A. M. Hassanabadi (2007). Non-cyclic graph of a group. Comm. Algebra. 35, 2057-2081
S. J. Baishya (2013). A note on finite C-tidy groups. Int. J. Group Theory. 2 (3), 9-17
L. Mousavi (2011). $n$-Cyclicizer groups. Bull. Iranian Math. Soc.. 37 (1), 161-170
D. Patrick and E. Wepsic (1991). Cyclicizers, centralizers and normalizers. Rose-Hulman Institute of Technology, Indiana, USA, Technical report, MS-TR 91-05.
K. O'Bryant, D. Patrick, L. Smithline and E. Wepsic (1992). Some facts about cycels and tidy groups. Rose-Hulman Institute of Technology, Indiana, USA, Technical report, MS-TR 92-04.
R. Schmidt (1970). Zentralisatorverbande endlicher Gruppen. Rend. Sem. Mat. Univ. Padova. 44, 97-131
R. Schmidt (1994). Subgroup Lattices of Groups. De Gruyter, Berlin.