Equation 677 Database

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Magma 5dd912467ab8…

magma 5dd912467ab8
Size
381
Isomorphism class hash
5dd912467ab88a31a69663f6faef1abc815c567aeb37a9819f28ec10457f8b6b
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 23:42:28
Display reorder
380,170,271,215,120,25,72,75,132,30,226,281,180,117,24,67,265,166,245,318,319,317,321,322,320,291,191,236,147,47,91,127,11,56,258,158,208,40,86,140,185,232,287,296,196,241,107,9,95,37,81,135,177,222,277,57,13,110,160,210,260,202,152,252,4,58,103,376,335,340,357,334,346,362,366,371,352,171,270,216,122,27,70,78,131,34,229,284,184,115,20,66,266,165,246,310,308,309,313,311,312,290,190,235,145,45,90,126,3,53,256,156,206,42,87,142,186,231,286,295,195,240,106,8,96,36,84,139,175,220,275,54,12,109,159,209,259,207,157,257,10,55,108,375,333,341,355,332,348,360,365,370,351,173,273,218,123,28,73,76,133,31,225,280,181,118,22,68,268,168,248,305,306,307,302,303,304,293,193,238,148,48,93,128,14,59,261,161,211,43,88,143,188,233,288,298,198,243,111,15,98,38,80,136,178,223,278,60,16,112,162,212,262,200,151,250,1,61,100,378,337,343,358,336,347,363,368,373,353,172,272,217,121,26,71,79,130,33,228,283,183,116,21,65,267,167,247,329,300,301,315,316,314,292,192,237,146,46,92,125,7,52,255,155,205,41,85,141,187,230,285,297,197,242,102,2,97,35,83,138,176,221,276,51,5,105,154,204,253,203,153,254,6,50,104,377,331,342,356,330,345,361,367,372,350,174,274,219,124,29,74,77,134,32,227,282,182,119,23,69,269,169,249,325,323,324,328,326,327,294,194,239,149,49,94,129,17,62,263,163,213,44,89,144,189,234,289,299,199,244,113,18,99,39,82,137,179,224,279,63,19,114,164,214,264,201,150,251,0,64,101,379,339,344,359,338,349,364,369,374,354 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#c3f553b30d54716d9e2e87cb9ed350bbbf2e522a2867abba1f7ef649b9b0800a, 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 23:42:29 · history