Equation 677 Database

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Magma 13381252e719…

magma 13381252e719
Size
595
Isomorphism class hash
13381252e7194064f427c2e04ba10be425241169536fe3bb68d76543caac318a
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
2026-10-06 22:27:29
Display reorder
38,37,39,40,41,36,328,327,329,331,332,330,378,377,376,381,379,380,362,361,360,358,359,357,399,398,397,401,402,400,519,510,512,520,580,301,300,303,304,305,302,57,56,58,59,54,55,66,71,67,68,69,70,182,181,183,178,179,180,210,209,211,212,213,208,104,103,105,106,107,102,20,19,21,22,23,18,12,17,13,14,15,16,191,190,192,193,194,195,241,240,242,243,244,245,319,318,320,322,323,321,317,316,315,314,312,313,368,367,366,364,365,363,373,375,374,372,370,371,466,465,505,506,468,467,403,480,436,479,435,478,530,523,526,525,529,533,554,569,551,574,572,582,583,581,586,579,136,135,132,133,134,137,24,29,25,26,27,28,226,225,227,222,223,224,188,187,189,184,185,186,76,75,77,72,73,74,144,143,145,146,147,142,230,229,231,232,233,228,173,172,174,175,176,177,63,62,64,65,60,61,121,120,122,123,124,125,455,454,407,495,501,494,492,499,493,489,490,491,504,461,500,460,423,424,483,440,441,442,443,444,390,389,388,392,393,391,339,474,428,472,427,473,542,521,518,540,541,517,576,585,562,548,559,568,577,558,556,557,108,113,110,111,112,109,292,291,293,288,289,290,270,275,271,272,273,274,237,236,238,239,234,235,276,281,277,278,279,280,7,6,8,9,10,11,219,140,138,139,220,141,117,116,118,119,114,115,129,128,130,131,126,127,166,171,167,168,169,170,410,408,409,413,411,412,336,338,337,333,334,335,382,384,383,387,385,386,308,307,306,310,311,309,487,486,508,406,509,488,471,326,470,507,469,325,536,537,513,516,514,515,590,584,545,591,553,560,561,593,567,570,259,258,261,262,263,260,266,265,267,268,269,264,252,257,253,254,255,256,155,154,156,157,158,159,51,50,52,53,48,49,5,4,1,0,2,3,150,149,151,152,153,148,200,199,201,196,197,198,95,94,90,91,92,93,31,30,32,33,34,35,477,433,434,395,396,394,341,340,342,344,345,343,350,349,348,346,347,429,453,485,405,484,452,451,352,351,353,354,355,356,422,420,502,498,503,421,528,532,535,534,511,543,588,564,546,547,589,571,563,544,552,550,249,248,251,246,247,250,218,217,221,214,215,216,297,296,298,299,294,295,207,206,202,203,204,205,96,101,97,98,99,100,86,85,87,88,89,84,79,78,80,81,82,83,285,284,286,287,282,283,163,162,164,165,160,161,42,47,43,44,45,46,497,457,456,458,459,496,482,438,439,404,437,481,449,448,450,445,446,447,430,475,369,476,431,432,417,419,418,416,414,415,324,462,425,464,426,463,539,538,527,524,531,522,594,573,549,578,587,592,555,575,565,566 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#40b1db721c17bf32e266eb97cd1492697125779c7804a195f580e3a793b1a85e, M = the submagma generated by {0, 66} (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 2026-10-06 22:27:30 · history