Equation 677 Database

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Magma e24a5fd8d5bd…

magma e24a5fd8d5bd
Size
381
Isomorphism class hash
e24a5fd8d5bd013e84f7b6a34964841b276f69b6d3fc1c455df08218ab1423d7
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:46:23
Display reorder
380,98,97,99,100,95,96,125,111,108,109,110,107,166,171,175,151,156,161,251,256,260,265,241,246,112,113,114,115,116,117,211,216,221,226,231,235,290,295,271,276,281,286,101,102,103,104,105,106,181,186,191,196,201,205,123,118,119,120,121,122,306,310,307,308,309,311,342,349,357,332,372,338,350,366,361,377,93,92,94,89,90,91,71,72,73,74,75,76,168,173,178,153,159,164,254,259,264,269,244,249,81,82,77,78,79,80,213,219,224,228,233,238,294,299,274,279,284,289,69,70,65,66,67,68,183,189,194,198,203,208,84,85,86,87,88,83,312,316,313,314,315,317,334,339,358,348,373,347,331,368,363,378,27,26,28,124,24,25,36,37,38,39,40,35,165,170,176,150,155,160,250,255,261,266,240,245,15,16,17,12,13,14,210,215,220,225,230,236,291,296,270,275,280,285,29,30,31,32,33,34,180,185,190,195,200,206,22,23,18,19,20,21,327,325,328,329,324,326,333,335,356,344,370,336,343,365,362,375,57,56,58,53,54,55,62,63,64,59,60,61,169,174,179,154,158,163,253,258,263,268,243,248,45,46,41,42,43,44,214,218,223,229,234,239,293,298,273,278,283,288,10,11,6,7,8,9,184,188,193,199,204,209,48,49,50,51,52,47,320,318,321,322,323,319,337,341,359,346,374,340,345,369,364,379,143,142,138,139,140,141,131,126,127,128,129,130,167,172,177,152,157,162,252,257,262,267,242,247,137,132,133,134,135,136,212,217,222,227,232,237,292,297,272,277,282,287,148,149,144,145,146,147,182,187,192,197,202,207,0,2,3,4,5,1,301,304,300,302,303,305,354,330,355,351,371,353,352,367,360,376 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#dc50bff4268d4e886a12bccb100fd4b53117610e2c07e48d4c792db14c6c3b47, M = {72} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 51.

last edited by qawbecrdtey at 2026-10-01 23:46:24 · history