Equation 677 Database

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Magma 5169602b19f8…

magma 5169602b19f8
Size
595
Isomorphism class hash
5169602b19f8bfd197a79d429a748ebffe5ed6e5c5ca2c6592b8cd9f1a6504c1
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 01:53:00
Display reorder
246,248,247,250,251,249,310,309,311,306,307,308,350,352,351,354,355,353,315,314,313,317,318,316,405,407,406,410,408,409,516,522,513,585,594,136,135,137,132,133,134,52,51,53,48,49,50,71,70,66,67,68,69,143,142,138,139,140,141,40,39,41,36,37,38,190,189,191,186,187,188,64,63,65,60,61,62,174,179,175,176,177,178,43,42,44,45,46,47,163,162,164,165,166,167,387,386,385,384,382,383,369,368,367,366,364,365,340,339,338,343,341,342,349,348,347,346,344,345,489,490,506,505,488,487,411,483,449,481,448,482,512,533,529,511,524,531,557,558,544,582,570,561,546,576,575,583,107,106,102,103,104,105,91,90,92,93,94,95,158,157,159,160,161,156,123,122,124,125,120,121,212,211,213,214,215,210,217,216,218,219,220,221,26,25,27,28,29,24,34,33,35,30,31,32,111,110,112,113,108,109,74,73,75,76,77,72,453,452,412,486,499,485,479,500,480,476,477,478,509,495,501,494,456,455,484,451,450,433,434,432,392,394,393,390,391,389,395,474,445,472,444,473,541,534,540,539,521,514,560,577,543,578,547,556,567,548,555,550,101,100,96,97,98,99,127,126,128,129,130,131,226,225,227,222,223,224,116,115,117,118,119,114,6,11,7,8,9,10,13,12,14,15,16,17,242,241,243,244,245,240,262,261,263,258,259,260,149,148,144,145,146,147,150,155,151,152,153,154,358,360,359,361,362,363,337,336,335,334,332,333,326,328,327,329,330,331,399,401,400,402,403,404,493,492,508,418,507,491,469,357,468,504,467,356,536,535,518,517,519,530,559,552,584,563,587,565,580,566,564,562,3,2,4,5,1,0,206,205,209,202,203,204,271,270,272,273,274,275,255,254,256,257,252,253,84,89,85,86,87,88,300,305,301,302,303,304,288,293,289,290,291,292,269,268,264,265,266,267,238,237,229,230,231,228,298,297,299,294,295,296,475,447,446,396,397,398,371,370,372,374,375,373,413,415,414,416,417,454,459,497,419,496,458,457,321,320,319,322,323,324,422,420,502,498,503,421,526,532,523,520,542,510,573,549,592,593,588,586,589,568,581,574,172,171,173,168,169,170,195,194,196,207,192,193,208,201,197,198,199,200,56,55,57,58,59,54,184,183,185,180,181,182,277,276,278,279,280,281,283,282,284,285,286,287,23,22,18,19,20,21,79,78,80,81,82,83,235,234,236,239,232,233,461,426,425,423,424,460,471,437,436,388,435,470,442,441,443,439,440,438,431,466,325,465,430,429,380,379,381,378,376,377,312,464,428,462,427,463,537,538,525,515,527,528,569,571,591,590,545,551,553,554,579,572 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#7c5787f3763007370795fcf378d2af7959e084037efbb89592fd99450acc2142, M = the submagma generated by {0, 48} (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 01:53:01 · history