Equation 677 Database

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Magma 64707d655f0f…

magma 64707d655f0f
Size
381
Isomorphism class hash
64707d655f0f783f34592391582548bb9b75f1f81234064f06223f79aaffa0f0
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 331 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:43:29
Display reorder
380,125,157,329,147,174,131,148,155,138,162,173,184,327,75,96,199,176,181,79,97,86,190,209,328,100,122,224,201,106,206,123,113,215,226,326,50,72,249,229,233,56,73,63,225,266,324,0,22,273,267,270,6,23,13,250,325,276,44,41,299,279,40,283,43,42,275,348,374,371,345,349,373,346,370,372,347,128,152,312,130,153,137,126,156,129,161,150,178,313,77,78,175,179,183,84,98,95,182,204,314,103,105,200,203,112,208,101,104,207,231,315,61,55,227,230,235,62,52,54,234,269,316,12,5,251,268,254,11,2,4,253,317,280,26,28,277,281,27,285,25,29,284,331,355,358,332,330,356,333,357,359,334,144,158,303,127,169,132,143,151,149,154,163,185,304,92,76,191,196,177,80,91,99,180,210,305,119,102,216,221,107,202,118,124,205,236,301,69,53,241,246,228,57,68,74,232,255,300,19,3,271,272,274,7,18,24,252,302,286,47,49,291,296,48,278,46,45,282,351,377,379,353,352,376,354,378,375,350,139,165,323,142,164,140,136,167,141,166,168,193,321,87,90,189,192,195,88,83,89,194,218,322,114,117,214,217,115,220,111,116,219,243,320,64,67,240,242,245,65,60,66,244,261,318,14,17,259,260,263,15,10,16,262,319,293,33,30,290,292,34,295,32,31,294,337,363,360,339,338,362,335,364,361,336,134,160,306,146,159,135,133,171,145,170,172,188,307,81,94,186,187,198,82,85,93,197,213,308,109,121,211,212,110,223,108,120,222,239,309,59,71,237,238,248,51,58,70,247,258,310,9,21,256,257,265,1,8,20,264,311,289,38,35,287,288,39,298,37,36,297,342,368,365,344,343,367,340,369,366,341 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#c9bcde453d03d05e9f11da444fb6ae6838e370d59ff71728dbabc87474ff704b, M = {66} 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:43:30 · history