Equation 677 Database

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Magma 7410107173cf…

magma 7410107173cf
Size
595
Isomorphism class hash
7410107173cf5ddd0a15d4ea7c19019809b5f22ae09b13b34c1e92ad39310e38
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 19:51:46
Display reorder
135,131,130,133,134,132,71,70,72,73,74,69,16,15,17,12,13,14,54,59,55,56,57,58,347,346,345,343,344,342,526,552,555,559,580,245,244,179,246,242,243,158,62,63,64,60,61,82,87,83,84,85,86,127,126,128,212,213,167,202,201,203,162,113,112,146,145,147,148,149,229,174,230,231,232,233,173,184,183,181,156,185,182,449,448,447,446,444,445,497,496,495,492,493,494,286,285,287,284,282,283,491,490,489,488,486,487,396,398,397,401,399,400,264,265,266,267,268,269,318,320,319,321,322,323,411,413,412,410,408,409,547,548,522,519,521,520,510,518,564,577,587,569,560,591,565,588,94,99,95,96,97,98,107,106,108,109,110,111,28,27,29,24,25,26,141,140,142,143,144,139,114,119,115,116,117,118,37,36,38,39,40,186,208,165,209,210,211,166,228,227,172,224,225,226,315,317,316,312,313,314,450,451,452,453,455,454,499,502,498,506,505,507,457,458,456,459,460,461,508,504,503,509,501,500,423,425,424,422,420,421,431,430,429,428,426,427,335,334,333,331,332,330,531,532,517,549,550,539,540,513,551,583,556,573,568,572,585,574,42,41,43,44,45,46,52,51,47,48,49,50,102,101,103,104,105,100,93,92,88,89,90,91,18,23,19,20,21,22,152,151,153,154,155,263,259,253,262,261,260,251,255,257,252,258,254,256,434,433,432,437,435,436,367,366,368,371,369,370,394,393,395,392,390,391,389,388,387,386,384,385,440,439,441,442,443,438,377,376,375,373,374,372,383,382,381,380,378,379,327,329,328,326,324,325,536,535,511,514,516,538,515,512,579,567,594,570,563,557,586,593,34,33,35,30,31,32,53,188,189,190,157,187,237,176,234,175,235,236,196,195,159,81,79,80,68,67,65,66,191,192,177,241,238,239,178,240,164,204,205,206,207,163,223,222,219,171,220,221,340,339,341,337,338,336,472,471,473,470,468,469,414,416,415,418,419,417,478,477,479,475,476,474,305,304,303,301,302,300,270,272,271,275,273,274,307,306,308,310,311,309,353,352,351,349,350,348,545,546,527,534,524,530,528,529,589,562,590,582,554,553,584,571,8,7,9,10,11,6,150,247,248,180,249,250,197,161,198,199,160,200,218,217,170,136,137,138,76,75,77,78,193,194,215,214,169,216,168,129,3,2,4,5,0,1,124,123,125,120,121,122,365,364,363,362,360,361,278,277,276,279,280,281,484,483,485,482,480,481,294,296,295,297,298,299,463,464,462,467,465,466,355,354,356,357,358,359,291,293,292,288,289,290,406,405,407,402,403,404,533,523,525,543,544,542,541,537,566,581,578,575,592,561,576,558 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#51f9b7d09d33f9fd9b24ec352fcf17309682f23da1a55124c3f963e5739f1055, M = the submagma generated by {0, 6} (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 19:51:47 · history