Equation 677 Database

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Magma b40f956f9365…

magma b40f956f9365
Size
595
Isomorphism class hash
b40f956f9365698924d8fc9cc7fa94b0814587828816aaf09103c06298187311
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 02:02:36
Display reorder
394,393,395,390,391,392,505,509,504,506,507,508,451,450,452,453,454,455,436,435,437,432,433,434,271,272,270,274,275,273,555,576,577,594,593,353,350,348,349,352,351,491,490,486,487,488,489,339,338,340,341,336,337,277,281,276,278,279,280,501,500,502,503,498,499,387,386,388,389,384,385,472,471,473,468,469,470,52,51,50,47,48,49,106,105,104,102,103,101,226,225,227,222,223,224,189,191,190,188,186,187,83,85,84,87,88,86,43,42,41,45,46,44,125,127,126,129,130,128,141,140,142,137,138,139,241,240,242,244,245,243,541,530,513,515,535,525,547,550,521,560,571,567,562,578,589,584,474,477,475,476,479,478,377,376,372,373,374,375,421,420,422,423,424,425,319,318,320,321,322,323,462,467,463,464,465,466,354,359,355,356,357,358,371,370,366,367,368,369,151,150,149,152,153,154,30,29,31,32,33,34,259,258,260,261,262,263,183,185,184,182,181,180,160,159,161,158,157,156,136,135,134,132,133,131,53,55,54,57,58,56,36,35,37,38,39,40,215,214,213,212,211,210,540,532,510,516,537,526,549,551,522,556,572,566,561,579,588,583,407,404,402,403,406,405,443,442,438,439,440,441,397,396,398,399,400,401,426,431,427,428,429,430,335,334,330,331,332,333,307,306,308,309,310,311,460,459,461,456,457,458,78,77,79,82,80,81,166,165,167,163,162,164,251,250,249,247,248,246,209,194,195,192,208,193,111,110,112,109,107,108,65,67,66,70,68,69,75,74,76,73,71,72,97,96,95,99,100,98,266,265,264,268,267,269,542,531,511,519,539,527,548,552,524,559,573,568,563,580,590,585,299,296,294,295,298,297,303,302,304,305,300,301,363,362,364,365,360,361,288,293,289,290,291,292,286,285,287,282,283,284,416,415,417,418,419,414,347,346,342,343,344,345,12,11,13,16,14,15,148,147,146,144,145,143,229,228,230,231,232,233,207,206,205,203,204,202,174,176,175,178,179,177,124,123,122,120,121,119,115,114,113,116,117,118,19,18,17,21,22,20,257,256,255,254,252,253,543,534,512,518,538,529,545,553,523,558,574,570,565,581,591,586,326,329,327,328,325,324,494,493,495,496,497,492,382,381,383,378,379,380,482,481,483,484,485,480,313,312,314,315,316,317,449,448,444,445,446,447,409,408,410,411,412,413,90,89,91,94,92,93,63,62,64,59,60,61,219,221,220,218,216,217,197,196,198,199,200,201,170,168,169,171,172,173,6,5,7,8,9,10,155,0,1,3,4,2,28,27,26,24,25,23,238,237,239,235,236,234,544,533,514,517,536,528,546,554,520,557,575,569,564,582,592,587 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#96b028d3c6de0cbaff964417289f690895c6af42769867ad5a7d2affbed8a752, M = the submagma generated by {0, 12} (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 02:02:37 · history