02501ntm a2200349 i 4500 vtls000104253 KUKTEM 20251117113410.0 180712s2018 my f am 000 0 eng d THE0000204(Local) 201905141025 nazirah 201807121544 saini UMP eng UMP rda FIST .S53 2018 r Thesis Shahoodh, Mohammed Khalid, author. Compatible actions for finite cyclic groups of p-power order / Mohammed Khalid Shahoodh Kuantan, Pahang : UMP, 2018 xi, 88 pages ; 30 cm. + 1 CD-ROM text rdacontent unmediated rdamedia computer rdamedia volume rdacarrier computer disc rdacarrier text file PDF rda Faculty of Industrial Sciences and Technology Thesis (Doctor of Philosophy) -- Universiti Malaysia Pahang – 2018 Includes bibliographical references The concept of the nonabelian tensor product of groups has its origins in the algebraic K-theory and the homotopy theory. This concept is defined on the actions which are compatible to each other. A different compatible pairs of actions can give a different nonabelian tensor products. Therefore, the maximum different nonabelian tensor product depends on the number of compatible pairs of actions. Thus, this research focuses on determining the number of compatible pairs of actions between two finite cyclic groups of p-power order, where p is an odd prime. This research starts with determining the necessary and sufficient conditions for the actions that have p-power order to be compatible. Then, the number of the automorphisms that have the p-power order for such type of groups, which present the actions are found. By the necessary and sufficient conditions, the number of the compatible pairs of actions has been determined according to the order of the action. Furthermore, the compatible action graph and its subgraph were introduced for the finite cyclic groups of p-power order. Then, some properties of the compatible action graph are also presented. Faculty of Industrial Sciences and Technology Dissertations Universities and colleges Disertations Theses 0 0 lcc 0 1 10000 10000 2019-09-04 0 FIST .S53 2018 r Thesis 0000123567 2019-09-04 00:00:00 1 2019-09-04 THESIS 0 0 lcc 0 1 10000 10000 2019-09-04 0 CD 11374 | FIST .S53 2018 r Thesis 0000123568 2019-09-04 00:00:00 1 2019-09-04 THESIS VIRTUA40 7971 7977 VTLSSORT0080*0200*0400*0900*1000*2450*2640*3000*3360*3370*3371*3380*3381*3470*5000*5020*5040*5200*6100*6500*6501*9992