Equation 677 Database

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Magma dd13525e9578…

magma dd13525e9578
Size
595
Isomorphism class hash
dd13525e9578dc59cd67a7515f91ee20d97960f5581b25ba1104a674f8979447
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 11:40:20
Display reorder
279,281,280,276,278,277,272,270,271,273,274,275,449,448,444,445,446,447,437,436,433,432,434,435,451,450,452,453,454,455,556,555,582,594,593,4,3,5,1,0,2,146,145,144,147,148,149,232,231,233,230,228,229,127,126,128,131,129,130,142,141,143,138,139,140,124,123,125,122,120,121,242,240,241,244,245,243,134,133,132,136,137,135,117,119,118,116,114,115,492,497,493,494,495,496,399,398,400,395,396,397,386,385,387,388,383,384,378,382,424,379,380,381,488,487,489,490,491,486,393,392,394,389,390,391,404,403,405,406,401,402,550,510,525,518,521,539,538,546,530,572,588,578,562,584,557,568,40,39,41,36,37,38,44,43,42,45,46,47,217,216,218,221,219,220,206,205,204,207,208,209,50,49,48,52,53,51,56,55,54,57,58,59,253,252,254,255,256,257,61,60,62,63,64,65,194,196,195,193,191,192,473,472,468,469,470,471,321,320,322,323,318,319,332,331,333,334,335,330,316,315,317,312,313,314,463,462,464,465,466,467,338,337,339,336,425,340,326,325,327,328,329,324,554,514,528,516,523,544,536,548,534,575,592,581,566,587,561,570,29,28,27,25,26,24,19,18,20,23,21,22,214,213,215,212,211,210,202,201,203,200,199,198,15,17,16,14,12,13,10,9,11,8,6,7,246,248,247,251,249,250,31,30,32,33,34,35,190,189,188,197,187,186,460,459,461,456,457,458,295,294,296,297,298,299,286,285,287,283,282,284,300,305,301,302,303,304,440,438,441,442,443,439,308,307,309,310,311,306,289,288,290,291,292,293,553,513,529,515,524,543,535,549,533,576,591,580,565,586,560,571,100,99,101,96,97,98,92,91,90,93,94,95,226,225,227,224,222,223,180,181,182,185,183,184,88,87,89,84,85,86,112,111,113,110,108,109,260,259,258,262,263,261,78,80,79,83,81,82,105,107,106,104,102,103,475,474,476,477,478,479,358,357,359,360,356,429,375,374,376,377,373,430,371,370,372,367,368,369,482,481,483,484,485,480,355,428,351,352,353,354,363,362,364,365,366,361,552,512,527,517,522,542,541,547,532,574,590,579,564,585,559,569,158,157,156,160,161,159,74,73,72,75,76,77,239,238,237,234,235,236,173,172,171,168,169,170,70,69,71,66,67,68,165,167,166,163,164,162,267,269,268,266,264,265,179,178,177,175,176,174,152,151,150,154,155,153,506,505,507,508,509,504,426,345,341,342,343,344,417,416,412,413,414,415,431,411,407,408,409,410,502,501,503,498,499,500,418,423,419,420,421,422,348,347,349,350,427,346,551,511,526,519,520,537,540,545,531,573,589,577,563,583,558,567 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#f04ca8125d7ce546c7552606527b36663a07f654279810fba8dfdb3271b338ee, M = the submagma generated by {48, 60} (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 11:40:22 · history