Equation 677 Database

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Magma 1a22ef42e7d5…

magma 1a22ef42e7d5
Size
595
Isomorphism class hash
1a22ef42e7d581982a5a003f17ba64fb05cff4f0714d1c36cf18015445dce199
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 09:22:59
Display reorder
89,88,90,91,92,87,137,136,138,139,134,135,61,60,62,57,58,59,392,391,390,394,395,393,326,325,324,328,329,327,534,510,584,566,572,244,241,174,245,243,242,153,10,11,12,8,9,63,68,64,65,66,67,21,20,22,186,187,155,183,182,184,154,13,14,141,140,142,143,144,220,171,233,234,235,232,170,194,193,195,158,196,197,413,412,411,409,410,408,496,495,494,493,491,492,443,442,441,438,440,439,355,354,356,358,359,357,364,363,365,362,360,361,436,435,437,432,434,433,264,263,265,266,267,268,502,503,498,505,501,504,549,550,526,514,524,525,513,516,585,558,586,590,561,557,555,593,28,31,29,30,27,32,82,81,83,84,85,86,75,80,76,77,78,79,120,119,121,122,123,124,110,109,105,106,107,108,18,17,19,15,16,185,214,165,215,216,217,166,225,224,168,226,222,223,497,489,490,487,486,488,272,274,273,269,270,271,499,506,500,507,508,509,350,349,348,353,351,352,453,455,454,450,452,451,425,424,423,422,421,420,306,308,307,311,309,310,459,461,460,456,458,457,530,536,519,548,551,520,533,521,579,571,553,582,581,563,588,556,97,94,98,93,96,95,6,5,1,2,3,4,42,41,43,44,39,40,35,34,36,37,38,33,74,73,69,70,71,72,146,145,147,148,149,257,256,246,248,250,249,221,255,254,247,251,252,253,449,448,447,445,446,444,381,383,382,378,379,380,430,429,431,427,426,428,339,341,340,336,337,338,330,332,331,334,335,333,316,315,317,313,314,312,418,417,419,414,415,416,387,389,388,385,386,384,539,541,515,527,522,528,529,518,554,562,594,587,560,552,591,569,127,130,128,129,126,125,111,204,205,202,161,203,200,160,201,159,198,199,219,218,167,133,131,132,26,25,24,23,240,192,173,238,239,236,172,237,156,188,189,190,191,157,231,230,227,169,228,229,305,304,303,301,302,300,479,478,477,476,474,475,343,342,344,345,346,347,369,371,370,366,367,368,372,374,373,376,377,375,396,398,397,399,400,401,275,277,276,280,278,279,471,473,472,469,470,468,547,545,532,538,523,531,517,511,583,565,592,568,559,573,589,580,47,50,48,49,46,45,7,180,181,152,178,179,210,164,211,212,163,213,207,206,162,112,113,114,117,116,118,115,208,209,175,176,150,177,151,0,103,102,104,99,100,101,56,55,51,52,53,54,467,466,465,462,464,463,319,318,320,322,323,321,481,480,482,483,484,485,290,292,291,287,288,289,294,293,295,298,296,297,281,283,282,284,285,286,402,404,403,407,405,406,299,258,259,260,261,262,537,535,540,546,544,543,542,512,575,577,567,570,578,564,574,576 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#92768bb2ce71adf5f3645437d2daad1854a25afcd5bf6e7bdc519de5c37f97ae, M = the submagma generated by {6, 24} (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 09:22:59 · history