Equation 677 Database

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Magma 17f23a5ce391…

magma 17f23a5ce391
Size
595
Isomorphism class hash
17f23a5ce391ea32c425403848efb519299f074c87f0f2f3619ef4f05e462eb6
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
2026-10-06 10:42:27
Display reorder
18,14,13,16,17,15,114,113,115,116,111,112,3,2,4,5,6,1,324,323,325,328,326,327,378,380,379,383,381,382,511,538,573,581,574,207,206,161,208,204,205,155,25,26,27,23,24,122,121,123,124,125,120,118,117,119,226,227,168,211,210,212,162,103,104,99,98,100,101,102,209,163,214,215,216,213,164,178,177,176,150,179,175,434,433,432,436,437,435,486,487,488,490,491,489,269,268,267,265,266,264,360,359,361,362,363,364,294,296,295,365,297,298,453,452,454,449,451,450,316,315,314,311,312,313,503,502,501,499,500,498,550,551,519,510,529,528,520,526,569,579,577,576,582,559,586,562,38,43,39,40,41,42,84,83,85,80,81,82,78,77,79,74,75,76,56,61,57,58,59,60,67,66,62,63,64,65,139,138,140,141,142,232,229,170,230,231,228,169,223,222,167,224,225,221,497,496,495,493,494,492,399,401,400,396,397,398,274,273,275,270,271,272,505,504,506,507,508,509,456,457,458,459,460,461,417,419,418,414,415,416,339,338,340,337,335,336,300,299,301,302,303,304,527,531,513,548,549,542,543,532,563,566,590,571,585,584,570,572,8,7,9,10,11,12,91,90,86,87,88,89,33,32,28,29,30,31,70,69,71,72,73,68,105,110,106,107,108,109,146,145,147,148,149,257,253,247,256,255,254,245,252,251,246,249,248,250,371,370,369,367,368,366,285,287,286,282,283,284,292,291,293,288,289,290,374,373,372,376,377,375,439,438,440,441,442,443,446,448,447,444,455,445,261,263,262,258,260,259,307,306,305,309,310,308,534,521,535,512,537,522,536,515,568,580,594,564,593,589,556,578,130,129,131,126,127,128,144,242,243,244,174,241,240,173,237,172,238,239,192,191,156,44,45,46,37,36,34,35,189,190,153,183,184,185,154,186,166,219,220,217,218,165,202,201,203,160,199,200,353,355,354,358,356,357,465,467,466,463,462,464,424,423,425,420,421,422,412,411,413,408,409,410,347,349,348,352,350,351,341,343,342,344,345,346,406,405,407,404,402,403,480,482,481,485,483,484,544,545,523,518,539,517,516,533,557,565,554,587,583,567,592,553,135,134,136,137,132,133,143,233,234,171,235,236,195,159,196,197,158,198,193,194,157,53,54,55,20,19,21,22,187,188,181,180,151,182,152,0,51,50,52,47,48,49,93,92,94,95,96,97,469,468,470,471,472,473,317,319,318,320,321,322,330,329,331,332,333,334,476,475,474,478,479,477,276,278,277,281,279,280,395,394,393,392,390,391,426,427,428,431,429,430,387,389,388,386,384,385,541,540,514,546,547,524,530,525,560,555,552,588,558,575,561,591 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#a68686773c1c84a50fc680c2f9bbdb3f90f3c80b3d983f347231cff070658488, M = the submagma generated by {0, 54} (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 2026-10-06 10:42:28 · history