Equation 677 Database

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Magma e860fa035e3d…

magma e860fa035e3d
Size
381
Isomorphism class hash
e860fa035e3d2395c805eb9b066d29f2973aba649966684f94d1ffe226ae857a
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:26:44
Display reorder
380,298,288,263,268,163,273,3,4,5,1,0,2,114,115,116,117,118,119,258,233,238,243,248,253,98,99,100,101,96,97,110,111,112,113,108,109,278,283,293,198,158,153,223,228,203,208,213,218,188,193,168,173,178,183,309,310,311,306,307,308,105,104,106,107,102,103,368,372,333,359,342,336,360,351,352,378,295,285,261,266,160,270,94,95,90,91,92,93,67,68,69,70,71,66,256,231,236,241,246,251,77,72,73,74,75,76,89,84,85,86,87,88,275,280,290,196,155,150,220,225,200,205,210,215,186,191,165,170,175,180,303,304,305,301,300,302,82,81,83,78,79,80,367,370,337,357,341,350,361,349,348,377,299,289,264,269,164,274,32,33,34,35,30,31,19,20,21,22,23,18,259,234,239,244,249,254,16,17,12,13,14,15,8,9,10,11,6,7,279,284,294,199,159,154,224,229,204,209,214,219,189,194,169,174,179,184,323,318,319,320,321,322,29,28,24,25,26,27,369,373,339,355,345,343,362,344,338,379,297,287,262,267,162,272,52,53,48,49,50,51,57,58,59,54,55,56,257,232,237,242,247,252,62,63,64,65,60,61,47,42,43,44,45,46,277,282,292,197,157,152,222,227,202,207,212,217,187,192,167,172,177,182,317,312,313,314,315,316,40,39,41,36,37,38,365,374,347,356,330,331,363,335,334,375,296,286,260,265,161,271,139,140,141,142,143,138,145,146,147,148,149,144,255,230,235,240,245,250,123,124,125,120,121,122,135,136,137,132,133,134,276,281,291,195,156,151,221,226,201,206,211,216,185,190,166,171,176,181,326,327,328,329,324,325,126,131,127,128,129,130,366,371,340,358,354,332,364,353,346,376 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#51f9fa4941789fcec91b298b71630f6443ab313fec0bf96b206088496fe3251b, M = {70} 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 23:26:45 · history