Equation 677 Database

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Magma 7ea9dd0a6e80…

magma 7ea9dd0a6e80
Size
381
Isomorphism class hash
7ea9dd0a6e80127a96c5ec76e2203d1d1e5884eca41f199ee610b81b197be26f
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 23:47:37
Display reorder
380,223,233,228,218,208,213,143,148,293,128,133,138,103,108,113,118,288,123,183,188,178,198,203,193,38,43,48,53,273,58,6,7,283,88,93,98,83,78,278,73,63,68,18,268,13,28,33,22,258,263,253,243,248,238,168,163,173,298,153,158,328,327,329,324,325,326,348,368,333,357,353,372,363,343,338,378,222,232,227,215,205,210,141,146,290,126,130,135,100,106,111,115,286,120,181,186,175,195,201,190,37,42,47,52,272,57,4,5,282,87,92,97,82,77,277,72,62,67,17,267,12,27,32,24,257,262,252,241,246,235,166,160,171,296,150,155,318,320,319,323,321,322,347,366,332,356,352,373,360,342,337,376,220,231,225,216,206,211,140,145,291,125,131,136,101,105,110,116,285,121,180,185,176,196,200,191,36,41,45,50,271,55,2,3,280,85,91,96,81,76,275,70,60,65,15,266,10,26,30,20,256,261,251,242,247,237,165,161,170,295,151,156,312,314,313,317,315,316,345,365,331,355,350,371,361,341,336,375,224,234,229,219,209,214,144,149,294,129,134,139,104,109,114,119,289,124,184,189,179,199,204,194,39,44,49,54,274,59,8,9,284,89,94,99,84,79,279,74,64,69,19,269,14,29,34,23,259,264,254,244,249,239,169,164,174,299,154,159,302,300,301,304,305,303,349,369,334,358,354,374,364,344,339,379,221,230,226,217,207,212,142,147,292,127,132,137,102,107,112,117,287,122,182,187,177,197,202,192,35,40,46,51,270,56,0,1,281,86,90,95,80,75,276,71,61,66,16,265,11,25,31,21,255,260,250,240,245,236,167,162,172,297,152,157,310,309,311,306,307,308,346,367,330,359,351,370,362,340,335,377 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#e6667989dcd92e07f9ac29d8b243d6a96a38fa8a609415f393f811e1aaa26c76, 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 23:47:38 · history