Equation 677 Database

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Magma 5dd37a89d603…

magma 5dd37a89d603
Size
595
Isomorphism class hash
5dd37a89d6034e1bcd57a8f68882a0f3162a8f8039907de5ef6193308330a329
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 04:04:48
Display reorder
221,217,216,219,220,218,213,212,214,215,210,211,314,316,315,318,319,317,343,342,341,338,339,340,331,330,329,328,326,327,521,513,515,569,574,256,255,257,252,253,254,167,166,162,163,164,165,48,53,49,50,51,52,34,33,35,30,31,32,25,24,26,27,28,29,99,98,100,101,96,97,3,2,4,5,1,0,122,121,123,124,125,120,187,186,188,189,190,191,238,237,239,234,235,236,390,392,391,395,393,394,360,362,361,363,364,365,378,380,379,383,381,382,367,366,368,369,370,371,471,472,505,504,469,470,313,460,423,462,424,461,531,530,520,518,517,528,546,570,545,585,544,563,553,554,561,579,272,271,273,274,275,270,247,246,248,249,250,251,192,197,193,194,195,196,15,14,16,17,12,13,244,243,245,240,241,242,128,127,129,130,131,126,176,175,177,178,179,174,139,138,140,141,142,143,110,109,111,112,113,108,309,308,310,311,306,307,453,452,418,492,501,491,479,500,480,476,477,478,509,490,499,489,450,451,473,436,435,434,432,433,320,322,321,323,324,325,312,465,426,464,425,463,541,526,539,519,510,540,564,568,580,589,584,550,555,543,583,594,227,226,222,223,224,225,134,133,135,136,137,132,266,265,267,268,269,264,277,276,278,279,280,281,68,67,69,70,71,66,82,81,83,78,79,80,201,200,202,203,198,199,42,47,43,44,45,46,23,22,18,19,20,21,103,102,104,105,106,107,372,374,373,377,375,376,359,358,357,356,354,355,385,384,386,387,388,389,334,333,332,336,337,335,485,484,507,415,506,483,488,417,487,508,486,416,535,536,511,514,529,512,588,571,587,575,581,565,548,590,582,549,287,286,282,283,284,285,77,76,72,73,74,75,299,298,294,295,296,297,117,116,118,119,114,115,62,61,63,64,65,60,6,11,7,8,9,10,147,146,148,149,144,145,54,59,55,56,57,58,205,204,206,207,208,209,94,93,95,90,91,92,468,430,431,351,352,353,409,410,408,411,412,413,398,400,399,397,396,437,446,475,401,474,445,444,348,347,349,345,346,344,422,420,502,498,503,421,533,542,534,525,524,522,592,567,558,572,559,566,557,551,547,556,85,84,86,87,88,89,185,184,180,181,182,183,291,290,292,293,288,289,228,233,229,230,231,232,173,172,168,169,170,171,260,259,261,262,263,258,40,39,41,36,37,38,158,157,159,160,161,156,301,300,302,303,304,305,154,153,155,150,151,152,494,456,457,454,455,493,481,448,447,414,449,482,438,440,439,443,441,442,429,467,350,466,428,427,405,407,406,403,402,404,419,496,458,497,459,495,537,538,516,532,523,527,591,586,562,573,552,593,560,578,577,576 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 {0, 66} (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 04:04:49 · history