Equation 677 Database

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Magma 1dc94feb8cac…

magma 1dc94feb8cac
Size
595
Isomorphism class hash
1dc94feb8cac455c8ccf60e0766d8ae1f68cb7d04b81c6bb3af25f65b0672f00
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 18:20:12
Display reorder
163,162,161,164,165,166,80,82,81,79,77,78,128,127,129,124,125,126,421,420,422,423,424,425,494,493,495,496,497,492,529,521,536,587,567,141,140,139,138,136,137,49,48,47,50,51,52,3,5,4,2,1,0,33,32,34,30,29,31,187,195,191,183,256,253,222,221,220,224,225,223,233,232,234,236,235,249,160,9,10,7,8,6,368,367,369,370,371,366,381,380,382,383,378,379,483,482,484,485,480,481,374,373,375,376,377,372,491,490,486,487,488,489,430,429,431,426,427,428,322,321,323,318,319,320,415,414,416,417,418,419,510,535,513,550,531,514,543,548,573,593,566,564,569,588,555,586,218,217,219,215,216,214,245,244,243,246,247,248,251,255,182,184,188,192,116,118,117,115,113,114,26,28,27,25,23,24,130,132,131,135,133,134,21,20,22,19,17,18,227,226,228,230,231,229,453,452,454,455,450,451,443,442,438,439,440,441,305,304,300,301,302,303,504,509,505,506,507,508,409,408,410,411,412,413,362,361,363,364,365,360,258,259,260,261,262,263,340,339,341,336,337,338,542,549,528,511,547,552,512,530,584,577,570,591,568,581,589,565,103,102,101,106,104,105,155,154,156,159,157,158,64,63,62,60,61,59,11,13,12,16,14,15,109,108,107,111,112,110,42,41,43,44,45,46,53,54,55,58,56,57,121,123,122,119,179,120,295,294,296,297,298,299,501,500,502,503,498,499,462,467,463,464,465,466,403,402,404,405,406,407,479,478,474,475,476,477,358,357,359,354,355,356,325,324,326,327,328,329,389,388,384,385,386,387,518,539,516,515,526,534,527,517,594,562,560,576,582,557,575,583,239,238,237,242,240,241,202,204,203,206,207,205,252,257,181,186,190,194,94,93,92,90,91,89,38,40,39,37,35,36,169,168,167,171,172,170,174,173,175,178,176,177,142,144,143,145,146,147,461,460,456,457,458,459,312,317,313,314,315,316,447,446,448,449,444,445,342,347,343,344,345,346,270,275,271,272,273,274,334,333,335,330,331,332,310,309,311,306,307,308,293,292,288,289,290,291,541,532,523,538,551,545,524,537,592,578,559,572,574,558,556,563,71,73,72,74,75,76,68,70,69,66,67,65,97,96,95,99,100,98,151,153,152,150,148,149,185,193,189,180,254,250,212,211,213,208,209,210,198,197,196,199,200,201,83,85,84,86,87,88,352,351,353,348,349,350,470,469,471,472,473,468,395,394,390,391,392,393,278,277,279,280,281,276,287,286,282,283,284,285,267,266,268,269,264,265,397,396,398,399,400,401,436,435,437,432,433,434,525,522,533,544,520,519,540,546,553,579,571,585,561,554,580,590 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 {36, 42} (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 18:20:13 · history