Equation 677 Database

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Magma 63c9058203a9…

magma 63c9058203a9
Size
409
Isomorphism class hash
63c9058203a94d93cefaf0754dd2d38ebe0389c0eb9570ce7b3866dd47d3cb8f
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 358 (nullity 51) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 00:28:31
Display reorder
408,402,407,400,404,405,406,401,403,172,20,395,59,97,122,147,45,297,347,322,197,222,247,272,372,173,21,396,60,98,123,148,46,171,19,394,58,96,121,146,44,170,18,393,71,95,120,145,43,298,348,323,198,223,248,273,373,299,349,324,199,224,249,274,374,296,346,321,196,221,246,271,371,174,24,397,74,99,124,149,49,295,345,320,195,220,245,270,370,158,7,382,63,82,107,132,32,283,333,308,183,208,233,257,358,159,8,383,55,83,108,133,33,157,6,381,54,81,106,131,31,161,10,385,65,85,110,135,35,284,334,309,184,209,234,258,359,285,335,310,185,210,235,259,360,282,332,307,182,207,232,256,357,160,9,384,64,84,109,134,34,286,336,311,186,211,236,260,361,154,2,378,51,78,103,128,27,278,328,303,178,203,229,253,353,155,4,379,52,79,104,129,29,152,1,376,61,75,100,125,26,153,3,377,50,77,102,127,28,280,330,305,180,205,225,269,355,281,331,306,181,206,231,255,356,276,326,301,175,201,226,251,351,156,5,380,53,80,105,130,30,279,329,304,179,204,230,254,354,168,17,392,70,92,117,142,42,293,343,318,193,218,243,267,368,150,22,399,72,93,118,143,47,167,16,391,69,91,116,141,41,169,23,398,73,94,119,144,48,294,344,319,194,219,244,268,369,277,327,302,177,202,228,252,352,292,342,317,192,217,242,266,367,151,0,375,62,76,101,126,25,275,325,300,176,200,227,250,350,165,14,389,68,89,114,139,39,289,339,314,189,214,239,263,364,166,15,390,57,90,115,140,40,164,13,388,67,88,113,138,38,163,12,387,56,87,112,137,37,290,340,315,190,215,240,264,365,291,341,316,191,216,241,265,366,288,338,313,188,213,238,262,363,162,11,386,66,86,111,136,36,287,337,312,187,212,237,261,362 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 409 = 9 + 5*80, 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 = P(11, 2, magma#2925dc18176c3a094e546f32ddfbde1b795255106b00f6076737cdc6da05a538, 8), M = {0, 1, 2, 3, 4, 5, 6, 7, 8} 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, 80): MacNeish's product over GF(16) x GF(5); 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. P(l, q, S, v) is the Paley pencil over Z/l with multiplier q on the seed S of order K + 1 with vertex v: S is relabelled with v as 0 and its other elements as 1..K in increasing order; the points are 0 (the vertex) and 1 + K x + t for (x, t) in Z/l x Z/K; points of one line, or a point and the vertex, multiply as in S (0 the vertex, t + 1 the point (x, t)); and (x, s)*(y, t) for x != y is ((1-q)x + qy, t) when y - x is a nonzero square mod l, else ((1-q)x + qy, -s-t mod K). Equation 255: satisfied. Idempotent elements: 1.

last edited by qawbecrdtey at 2026-10-08 00:28:32 · history