Equation 677 Database

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Magma 8649fad7753c…

magma 8649fad7753c
Size
595
Isomorphism class hash
8649fad7753c67e9a45da8294cb3d718c3688ca50f0d78ae398453bf1820782c
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 09:22:51
Display reorder
276,277,278,281,279,280,275,274,273,270,272,271,328,327,329,324,325,326,334,333,335,330,331,332,336,341,337,338,339,340,555,556,593,594,582,200,199,198,203,201,202,188,187,186,190,191,189,265,264,266,267,268,269,208,207,209,205,204,206,61,60,62,63,64,65,76,75,77,74,72,73,219,221,220,218,216,217,68,67,66,69,70,71,193,192,194,196,197,195,499,498,500,501,502,503,505,504,506,507,508,509,320,319,321,322,323,318,347,346,342,343,344,345,357,356,358,359,354,355,494,493,495,496,497,492,351,350,352,353,348,349,554,544,514,549,518,539,534,529,524,576,586,566,571,581,592,561,22,21,23,19,20,18,115,114,116,117,118,119,250,249,251,246,247,248,13,12,14,15,16,17,128,127,126,130,131,129,134,133,132,135,136,137,226,225,227,222,223,224,124,123,125,122,120,121,111,113,112,108,109,110,398,397,399,400,401,396,292,291,293,288,289,290,411,410,412,413,408,409,424,423,425,420,421,422,417,416,418,419,414,415,402,407,403,404,405,406,428,427,429,430,431,426,553,543,511,548,517,535,531,528,523,575,584,565,570,580,591,560,78,80,79,81,82,83,98,97,96,100,101,99,258,260,259,263,261,262,89,88,87,85,86,84,31,30,32,33,34,35,94,93,95,92,90,91,210,211,212,213,214,215,27,29,28,25,26,24,103,102,104,106,107,105,385,384,386,387,388,389,365,364,360,361,362,363,295,294,296,297,298,299,382,381,383,378,379,380,375,374,376,377,372,373,395,394,390,391,392,393,369,368,370,371,366,367,550,541,512,545,515,537,533,525,520,572,587,563,567,577,589,558,36,38,37,39,40,41,160,159,161,156,157,158,253,252,254,255,256,257,46,45,47,42,43,44,144,146,145,149,147,148,150,152,151,154,155,153,233,232,231,229,230,228,143,142,141,138,139,140,165,167,166,162,163,164,464,463,465,466,467,462,301,300,302,303,304,305,437,436,432,433,434,435,444,449,445,446,447,448,443,442,438,439,440,441,459,458,460,461,456,457,454,453,455,450,451,452,552,540,510,547,519,536,532,526,522,574,585,564,569,578,588,559,10,9,11,7,8,6,59,58,57,55,56,54,243,245,244,242,241,240,0,1,2,3,4,5,174,176,175,179,177,178,168,170,169,172,173,171,239,238,237,235,236,234,181,180,182,185,183,184,48,50,49,51,52,53,316,315,317,312,313,314,282,283,284,285,286,287,486,491,487,488,489,490,480,485,481,482,483,484,479,478,474,475,476,477,309,308,310,311,306,307,472,471,473,468,469,470,551,542,513,546,516,538,530,527,521,573,583,562,568,579,590,557 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#f44078deebe7730562c927e2829a32c42b90cd1087b6200dbe445a4d4d2f9fa6, M = the submagma generated by {6, 60} (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 09:22:52 · history