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We investigate conditions on an infinite simple group in order to construct a zero-symmetric nearring with identity on it. Using the Higman-Neumann-Neumann extensions and Clay’s characterization, we obtain zero-symmetric nearrings with identity with the additive groups infinite simple groups. We also show that no zero-symmetric nearring with identity can have the symmetric group as its additive group.
Let be a subgroup of a finite group . We say that satisfies the -property in if for any chief factor of , is a -number. We study the influence of some -subgroups of satisfying the -property on the structure of , and generalize some known results.
Let be some partition of the set of all primes , be a finite group and . A set of subgroups of is said to be a complete Hall -set of if every non-identity member of is a Hall -subgroup of and contains exactly one Hall -subgroup of for every . is said to be -full if possesses a complete Hall -set. A subgroup of is -permutable in if possesses a complete Hall -set such that = for all and all . A subgroup of is -permutably embedded in if is -full...
We introduce a new subgroup embedding property of finite groups called CSQ-normality of subgroups. Using this subgroup property, we determine the structure of finite groups with some CSQ-normal subgroups of Sylow subgroups. As an application of our results, some recent results are generalized.
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