Equation 677 Database

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Magma 14d9110710eb…

magma 14d9110710eb
Size
595
Isomorphism class hash
14d9110710eb0831b6fcfcbcfe134b92f2e8c923f35aab6844c9fd5f42aeb0fd
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 17:53:30
Display reorder
136,135,137,138,133,134,55,54,56,57,58,53,119,118,120,121,122,117,430,429,428,427,425,426,360,361,448,363,364,362,522,539,590,582,571,188,187,153,189,185,186,162,76,77,78,74,75,5,4,0,1,2,3,89,88,90,217,218,164,222,221,220,165,102,103,19,18,20,21,22,184,170,233,234,235,232,169,200,199,201,158,202,198,504,506,505,509,507,508,411,410,409,407,408,406,272,271,273,274,275,276,347,346,345,344,342,343,502,501,503,500,498,499,332,331,330,334,335,333,451,450,452,264,461,449,456,390,389,391,392,393,548,551,513,532,514,531,533,542,570,574,558,567,566,560,584,559,32,31,33,34,29,30,37,38,39,40,35,36,45,44,46,41,42,43,112,111,113,114,115,116,104,109,105,106,107,108,95,94,91,92,93,219,214,161,211,212,213,160,183,182,152,179,180,181,288,287,286,284,285,283,434,433,435,431,457,432,496,495,497,492,493,494,488,486,487,491,489,490,445,444,443,446,447,442,372,371,373,374,375,376,278,277,279,280,281,282,262,261,263,258,260,259,526,521,524,549,550,534,543,525,580,576,572,592,593,581,575,589,68,67,69,64,65,66,7,8,9,10,11,6,27,26,28,23,24,25,83,82,84,85,86,87,48,47,49,50,51,52,146,145,147,148,149,257,252,246,253,254,255,231,256,248,247,249,250,251,423,422,424,460,454,455,421,453,420,418,419,417,341,340,339,337,338,336,311,310,312,308,309,307,400,402,401,404,405,403,300,299,298,296,297,295,394,396,395,399,397,398,302,301,303,305,306,304,541,512,527,528,529,530,519,520,569,556,594,555,554,583,579,563,141,140,142,143,144,139,110,223,224,225,166,226,191,154,192,155,193,190,242,241,172,125,123,124,71,70,72,73,210,209,157,196,197,194,156,195,151,177,178,176,175,150,237,236,238,171,239,240,470,480,479,471,481,482,294,293,292,290,291,289,324,323,322,320,321,319,367,366,365,370,368,369,464,463,462,465,466,485,313,315,314,318,316,317,328,327,329,325,326,458,437,436,438,440,441,439,545,547,537,517,515,518,523,538,586,564,561,577,553,585,587,591,12,17,13,14,15,16,59,206,203,159,204,205,227,168,228,229,167,230,216,215,163,80,81,79,62,61,63,60,207,208,244,243,173,245,174,126,129,128,130,131,132,127,96,101,97,98,99,100,359,358,357,355,356,354,350,349,348,352,353,351,484,483,472,475,474,473,476,467,477,468,469,478,380,382,381,378,379,377,268,270,269,267,265,266,415,414,416,459,412,413,387,386,388,384,385,383,535,516,511,546,544,536,510,540,568,562,588,565,578,573,552,557 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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#3577482bd341efd08404d9d1bdf0973fd33301f1401bf0112f6bd2c4e9ff916f, M = the submagma generated by {30, 42} (35 elements) 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, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-07 17:53:31 · history