Equation 677 Database

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Magma fd13eb354964…

magma fd13eb354964
Size
595
Isomorphism class hash
fd13eb3549648ec94a6ecea8ad382850ac7fd3e1ac4daeb4747645af3714dbc4
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 08:10:10
Display reorder
238,237,239,234,235,236,113,112,114,115,116,117,417,416,418,413,415,414,392,391,390,389,387,388,409,407,408,410,411,412,521,520,530,581,557,203,199,200,201,202,198,7,6,8,9,10,11,134,133,135,130,131,132,283,282,284,285,286,287,289,288,290,291,292,293,268,267,269,264,265,266,95,94,96,97,98,99,230,229,231,232,233,228,159,158,160,161,156,157,51,50,46,47,48,49,355,357,356,358,359,360,369,368,367,371,372,370,322,321,323,325,326,324,339,341,340,382,342,383,472,471,505,504,473,470,319,462,426,464,427,463,531,522,527,525,533,528,552,553,591,572,587,578,565,550,560,590,43,45,40,41,42,44,38,37,39,34,35,36,162,167,163,164,165,166,210,215,211,212,213,214,190,189,191,186,187,188,59,58,60,61,62,63,149,148,144,145,146,147,185,184,180,181,182,183,56,55,57,52,53,54,105,104,100,101,102,103,435,434,381,478,500,477,496,501,497,495,493,494,507,487,499,486,450,449,485,445,444,447,448,446,404,403,405,400,401,402,320,465,428,467,429,466,541,534,540,513,539,510,576,562,575,548,547,569,545,554,566,574,173,169,170,171,172,168,31,30,32,33,28,29,153,152,154,155,150,151,300,305,301,302,303,304,109,108,110,111,106,107,12,17,13,14,15,16,21,142,19,20,141,18,92,91,93,88,89,90,208,207,209,204,205,206,174,179,175,176,177,178,374,373,375,377,378,376,312,314,313,317,315,316,347,346,348,344,345,343,351,350,349,353,354,352,490,489,509,406,508,488,474,379,475,506,476,380,535,536,512,514,515,516,561,544,580,567,543,551,573,568,564,593,126,128,129,124,125,127,220,219,221,216,217,218,310,309,311,306,307,308,242,241,243,244,245,240,255,254,256,257,252,253,72,71,73,74,75,70,68,67,69,64,65,66,280,279,281,276,277,278,80,79,81,76,77,78,4,3,5,1,0,2,479,436,437,385,386,384,393,395,394,398,396,397,330,329,331,327,328,430,459,492,419,491,458,457,334,333,335,336,337,338,422,420,502,498,503,421,532,523,511,526,519,542,577,549,585,558,570,589,556,584,594,582,259,261,262,263,258,260,139,138,140,143,136,137,270,275,271,272,273,274,294,299,295,296,297,298,224,223,225,226,227,222,83,82,84,85,86,87,121,120,122,123,118,119,196,195,197,192,193,194,246,251,247,248,249,250,27,26,22,23,24,25,484,443,442,441,440,483,460,424,423,318,425,461,454,456,455,451,452,453,431,468,332,469,432,433,362,361,363,364,365,366,399,480,438,482,439,481,538,537,517,518,524,529,559,555,579,586,563,571,583,546,588,592 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#10604212f7d4a7b51fd21a22d9c743e5a67297285884dbf7fd2d260472af6645, M = the submagma generated by {42, 48} (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 08:10:11 · history