Equation 677 Database

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Magma 4c50cc1b42f8…

magma 4c50cc1b42f8
Size
381
Isomorphism class hash
4c50cc1b42f8b6e25e31ceaeda3b8a949cb1c0daed6eba887b5eb651845c3569
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 23:49:01
Display reorder
380,196,186,206,216,226,236,36,41,16,21,26,31,290,241,251,261,271,281,65,70,46,51,56,60,102,112,8,0,2,91,106,116,80,85,75,96,170,121,131,141,151,161,314,315,312,321,322,313,175,125,135,145,155,165,277,297,247,267,257,287,210,220,230,181,190,200,339,351,363,358,369,342,378,373,349,341,197,187,207,217,227,237,37,42,17,22,27,32,292,242,252,262,272,282,67,72,47,52,57,62,100,110,3,4,1,92,107,117,82,87,77,97,173,123,133,143,153,163,324,325,326,327,328,329,177,127,137,147,157,167,275,296,245,265,255,285,213,223,233,183,193,203,340,354,362,355,368,343,377,372,345,338,195,185,205,215,225,235,35,40,15,20,25,30,291,240,250,260,270,280,66,71,45,50,55,61,101,111,5,6,7,90,105,115,81,86,76,95,172,122,132,142,152,162,306,307,308,309,310,311,176,126,136,146,156,166,276,295,246,266,256,286,212,222,232,182,192,202,335,352,360,359,367,334,375,371,348,336,198,188,208,218,228,238,38,43,18,23,28,33,293,243,253,263,273,283,68,73,48,53,58,63,103,113,11,9,10,93,108,118,83,88,78,98,171,120,130,140,150,160,320,323,316,317,318,319,178,128,138,148,158,168,278,298,248,268,258,288,211,221,231,180,191,201,330,350,364,356,366,331,379,374,346,333,199,189,209,219,229,239,39,44,19,24,29,34,294,244,254,264,274,284,69,74,49,54,59,64,104,114,12,13,14,94,109,119,84,89,79,99,174,124,134,144,154,164,300,302,303,304,305,301,179,129,139,149,159,169,279,299,249,269,259,289,214,224,234,184,194,204,332,353,361,357,365,337,376,370,347,344 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#e7d843eeb4140ee4f2ae7f87ad1590cd2b2e584cf01474530a75f9f611790378, M = {73} 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 23:49:02 · history