Equation 677 Database

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Magma 95419d9a9019…

magma 95419d9a9019
Size
595
Isomorphism class hash
95419d9a9019d7328fff7c6aa6035995a698c6a49ae8b31e034f978ea5dd3cdb
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
2026-10-08 17:31:39
Display reorder
51,50,46,47,48,49,115,114,116,117,118,113,68,67,69,64,65,66,448,467,447,445,446,444,413,412,411,408,409,410,517,521,561,568,587,244,243,174,245,241,242,172,142,140,141,144,143,81,80,76,77,78,79,30,29,31,212,211,163,218,217,219,166,44,45,109,108,110,111,112,229,170,233,230,231,232,169,184,183,185,153,186,187,335,337,336,333,334,332,495,497,496,494,492,493,365,364,366,361,362,363,260,258,259,261,262,263,491,490,489,486,487,488,420,422,421,425,423,424,325,324,323,321,322,320,436,435,437,433,434,432,550,548,523,525,510,528,520,524,557,581,560,559,569,583,571,593,52,57,53,54,55,56,40,43,41,42,39,38,1,0,2,3,4,5,124,123,119,120,121,122,107,106,102,103,104,105,17,16,18,19,20,190,201,159,202,199,200,158,195,194,155,191,192,193,503,501,502,500,498,499,306,308,307,305,303,304,297,299,298,302,300,301,505,507,506,504,509,508,465,464,466,463,461,462,370,372,371,369,367,368,377,376,378,373,374,375,454,456,455,457,458,459,533,532,511,549,551,516,531,512,588,586,580,584,582,590,575,585,82,87,83,84,85,86,25,22,26,21,24,23,62,61,63,58,59,60,135,134,136,137,138,139,133,132,128,129,130,131,146,145,147,148,149,257,250,247,251,248,249,224,256,255,246,252,253,254,484,483,482,479,480,481,429,426,431,427,428,430,485,309,310,311,312,313,316,315,314,317,318,319,338,340,339,342,343,341,394,396,395,393,391,392,348,347,349,344,345,346,269,268,267,272,270,271,537,514,538,539,541,542,540,522,591,594,553,554,563,574,565,572,34,33,35,36,37,32,6,181,179,180,152,182,177,150,178,151,176,175,235,234,171,125,126,127,100,99,101,98,227,228,168,222,223,220,167,221,164,216,213,214,215,165,240,239,236,173,237,238,360,359,358,355,356,357,284,283,282,280,281,279,398,397,399,400,401,402,405,404,403,406,407,460,469,468,470,266,264,265,418,417,419,414,415,416,449,450,476,453,451,452,478,350,351,353,354,352,547,544,535,518,519,536,529,526,589,562,579,558,592,566,567,564,88,93,89,90,91,92,28,208,207,162,210,209,206,161,203,204,160,205,189,188,154,9,7,8,95,94,96,97,225,226,198,197,156,196,157,27,10,15,11,12,13,14,71,70,72,73,74,75,286,285,287,290,288,289,385,387,386,390,388,389,383,382,384,379,380,381,326,328,327,330,331,329,296,295,294,291,292,293,278,277,276,274,275,273,474,473,475,477,471,472,443,442,441,440,438,439,534,515,543,546,545,513,530,527,552,555,578,556,570,576,577,573 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 {24, 54} (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 2026-10-08 17:31:42 · history