Equation 677 Database

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Magma 3c293056bcfd…

magma 3c293056bcfd
Size
595
Isomorphism class hash
3c293056bcfdd6ff2c2d110119d302867b1916a24f7b92bbcae6fc1c92c40919
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 20:11:56
Display reorder
93,92,88,89,90,91,53,58,54,55,56,57,17,16,12,13,14,15,51,50,52,47,48,49,387,389,388,386,384,385,528,571,563,583,562,251,247,180,249,250,248,177,150,146,147,148,149,121,120,116,117,118,119,66,65,67,201,200,162,222,221,223,170,114,115,138,137,139,140,141,231,176,236,239,237,238,175,183,182,181,156,184,185,447,449,448,446,444,445,377,376,373,372,370,371,492,494,493,496,497,495,360,359,358,361,362,363,490,489,491,487,488,486,461,460,459,457,458,456,410,409,408,413,411,412,427,426,428,429,430,431,548,547,536,537,523,517,521,518,580,579,576,588,585,591,574,593,83,85,84,87,82,86,10,9,11,6,7,8,69,74,70,71,72,73,33,32,34,35,30,31,131,130,132,133,128,129,38,37,39,40,36,195,187,158,188,189,186,157,191,190,159,192,193,194,479,478,477,475,476,474,327,329,328,324,325,326,380,379,378,381,382,383,455,454,453,450,451,452,342,344,343,345,346,347,504,506,505,503,502,499,311,310,309,308,306,307,498,507,500,509,501,508,530,529,513,549,550,525,524,526,561,582,554,552,567,553,560,570,123,125,124,127,122,126,99,98,94,95,96,97,64,63,59,60,61,62,80,79,81,76,77,78,19,18,20,21,22,23,152,151,153,154,155,263,258,253,259,260,261,242,256,255,252,262,257,254,340,339,341,336,337,338,467,466,465,464,462,463,290,289,288,291,292,293,484,483,485,482,481,480,276,278,277,279,280,281,365,364,366,367,368,369,348,350,349,351,352,353,402,404,403,407,405,406,538,541,516,520,511,515,519,512,557,568,569,590,594,572,586,581,44,46,45,42,43,41,75,212,213,210,166,211,197,160,198,161,199,196,225,224,171,136,134,135,143,142,144,145,240,241,179,243,245,246,178,244,165,209,206,207,208,164,229,228,230,172,226,227,305,304,303,301,302,300,299,298,297,296,294,295,424,423,425,422,420,421,419,418,417,414,415,416,282,284,283,285,286,287,270,272,271,275,273,274,332,331,330,335,333,334,265,266,264,269,267,268,546,545,532,522,533,527,531,514,565,589,584,564,592,566,555,556,1,3,2,5,0,4,68,204,205,163,202,203,235,174,232,233,173,234,217,216,167,110,111,112,101,100,102,103,215,214,218,220,168,219,169,113,28,27,29,24,25,26,107,106,108,109,104,105,316,315,317,312,313,314,391,390,392,394,395,393,375,357,374,356,354,355,468,470,469,472,473,471,322,321,323,319,320,318,397,396,398,399,400,401,440,439,438,443,441,442,436,435,437,432,433,434,510,542,539,544,543,535,534,540,587,573,577,558,578,559,575,551 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#51f9b7d09d33f9fd9b24ec352fcf17309682f23da1a55124c3f963e5739f1055, M = the submagma generated by {6, 24} (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 20:11:58 · history