Equation 677 Database

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Magma 7d0682d738f9…

magma 7d0682d738f9
Size
595
Isomorphism class hash
7d0682d738f9cce3c75c2c50f0a8aaa4b84c346776369a9077d59e18d2a4f441
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 13:29:41
Display reorder
105,102,106,107,104,103,12,11,13,14,15,16,50,49,51,52,53,48,363,365,364,361,362,360,331,330,332,333,334,335,517,515,560,565,577,243,242,174,244,245,241,162,112,108,109,110,111,59,58,54,55,56,57,89,88,90,210,209,161,220,219,221,167,114,115,6,10,7,8,9,180,170,234,232,233,226,171,185,184,181,152,182,183,505,504,506,508,509,507,323,322,321,318,319,320,403,404,402,405,407,406,373,372,374,375,376,377,397,396,398,400,401,399,299,298,297,296,294,295,449,427,426,430,428,429,500,499,498,503,501,502,550,549,512,511,523,513,521,522,561,571,593,582,554,578,553,558,25,24,20,21,22,23,61,60,62,63,64,65,43,42,44,45,46,47,35,34,30,31,32,33,80,79,81,76,77,78,93,92,94,95,91,211,196,156,197,198,195,155,192,191,154,188,189,190,408,410,409,445,443,444,436,435,434,431,432,433,338,337,336,339,340,341,495,497,496,494,492,493,270,272,271,273,274,275,347,346,345,344,342,343,489,491,490,487,486,488,456,457,458,460,461,459,535,526,516,551,548,524,518,519,557,562,567,572,573,563,555,586,101,100,96,97,98,99,123,128,124,125,126,127,134,133,129,130,131,132,39,38,40,41,36,37,0,5,1,2,3,4,146,145,147,148,149,257,255,246,256,248,249,175,254,253,247,250,251,252,411,413,412,448,446,447,442,441,440,437,438,439,302,301,300,303,304,305,308,307,306,310,311,309,269,268,267,266,264,265,315,317,316,312,313,314,351,353,352,348,349,350,393,395,394,390,391,392,540,541,534,533,530,532,531,510,588,575,574,552,594,587,580,570,140,139,135,136,137,138,75,208,205,206,160,207,179,151,176,150,177,178,200,199,157,68,66,67,143,142,144,141,240,235,172,239,236,237,173,238,159,203,204,201,202,158,230,229,231,169,227,228,474,479,480,475,481,482,282,284,283,286,287,285,422,421,420,423,424,425,359,358,357,355,356,354,450,452,451,453,454,455,262,261,263,258,260,259,418,417,419,415,416,414,469,468,484,483,485,470,545,547,536,528,520,525,529,527,559,564,589,591,592,568,590,569,70,69,71,72,73,74,122,224,225,168,222,223,212,163,213,214,164,215,186,187,153,17,18,19,27,26,28,29,194,193,217,216,165,218,166,113,117,116,118,119,120,121,82,87,83,84,85,86,289,288,290,292,293,291,370,369,371,368,366,367,379,378,380,383,381,382,478,473,477,471,472,476,325,324,326,328,329,327,386,385,384,389,387,388,462,464,463,465,466,467,277,276,278,280,281,279,542,543,514,544,546,537,538,539,579,576,566,556,581,585,583,584 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#d668bf04c36f8b4c67728650c5c82a046d470936a3c130394e60cdea0aa42f4e, M = the submagma generated by {0, 12} (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 13:29:42 · history