Equation 677 Database

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Magma 4b4e779cae78…

magma 4b4e779cae78
Size
595
Isomorphism class hash
4b4e779cae786ac01a424dc71505a3c58bf4790467c8caf83c7af21769e3741d
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 00:43:52
Display reorder
320,319,321,324,322,323,360,359,361,358,446,357,432,431,430,427,428,429,389,391,390,387,388,386,396,395,397,393,394,392,525,512,535,522,536,504,485,459,506,505,458,482,434,433,436,435,447,451,453,452,449,450,448,401,400,399,494,467,398,488,489,316,463,317,318,314,313,315,311,312,462,18,23,19,20,21,22,188,187,189,190,191,186,205,204,206,207,208,209,166,165,167,162,163,164,129,128,130,131,126,127,226,225,227,222,223,224,261,260,262,263,258,259,42,47,43,44,45,46,117,116,118,119,114,115,75,74,76,77,72,73,526,519,539,531,530,527,559,550,588,552,580,577,583,568,573,564,370,369,371,372,373,368,330,329,331,333,334,332,424,426,425,422,423,421,374,376,375,377,378,379,416,415,417,413,414,412,437,439,438,327,328,493,113,112,108,109,110,111,37,36,38,39,40,41,266,265,267,268,269,264,13,12,14,15,16,17,97,96,98,99,100,101,195,194,196,197,192,193,53,52,48,49,50,51,136,135,137,132,133,134,85,84,86,87,88,89,147,146,148,149,144,145,523,520,513,529,528,514,553,572,563,558,589,549,578,567,548,555,353,352,354,355,356,351,346,345,347,349,350,348,364,363,362,365,366,367,380,382,381,383,384,385,308,310,309,305,306,307,302,304,303,300,301,509,82,81,83,78,79,80,200,199,201,202,203,198,161,160,156,157,158,159,247,246,248,249,250,251,277,276,278,279,280,281,285,284,286,287,282,283,59,58,54,55,56,57,212,211,213,214,215,210,138,143,139,140,141,142,107,106,102,103,104,105,544,540,511,516,518,517,566,581,565,570,571,579,591,557,586,556,444,443,442,440,441,445,404,470,471,498,405,497,475,477,476,479,480,478,502,483,481,420,418,419,454,456,455,457,503,484,460,507,508,461,486,487,291,290,292,293,288,289,151,150,152,153,154,155,273,272,274,275,270,271,35,34,30,31,32,33,228,233,229,230,231,232,7,6,8,9,10,11,255,254,256,257,252,253,219,218,220,221,216,217,60,65,61,62,63,64,296,295,297,298,299,294,543,537,532,521,510,515,561,582,587,546,590,569,547,592,551,584,340,339,344,342,343,341,325,490,464,326,491,492,411,474,501,473,410,500,499,409,472,406,407,408,337,336,335,338,465,466,496,495,468,469,402,403,28,27,29,24,25,26,240,245,241,242,243,244,185,184,180,181,182,183,0,1,2,3,4,5,169,168,170,171,172,173,179,178,174,175,176,177,90,95,91,92,93,94,123,122,124,125,120,121,239,238,234,235,236,237,70,69,71,66,67,68,524,534,542,541,533,538,585,562,554,560,576,545,575,593,594,574 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#ca4e87f44b5aa8ee937e3111d7e18929d38c701d18b6266af0f19751e7c29bcd, M = the submagma generated by {6, 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 2026-10-08 00:43:54 · history