Equation 677 Database

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Magma b7a5323c2eaa…

magma b7a5323c2eaa
Size
381
Isomorphism class hash
b7a5323c2eaa093e9889be82b1b826134adea4cb05303461a5dce1c1f51ba848
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 23:39:23
Display reorder
380,140,136,145,25,20,291,307,308,306,310,311,309,295,165,171,161,151,156,93,88,278,80,72,78,98,103,108,11,10,283,182,187,177,197,202,192,120,111,116,130,125,286,231,221,226,215,206,210,46,265,51,31,35,44,4,271,5,65,61,55,241,236,245,250,255,260,371,365,341,335,331,353,348,361,356,378,143,138,148,26,23,293,318,319,320,321,322,323,298,168,173,163,153,158,91,85,276,81,71,76,95,100,105,0,1,281,180,185,175,196,201,191,123,113,118,133,128,288,232,222,227,217,207,212,47,267,52,32,37,40,12,272,13,67,62,57,243,238,247,252,257,262,374,368,342,337,332,351,346,363,358,376,144,139,149,29,24,294,317,315,316,314,312,313,299,169,174,164,154,159,94,89,279,84,74,79,99,104,109,18,19,284,184,189,179,199,204,194,124,114,119,134,129,289,234,224,229,219,209,214,49,269,54,34,39,43,16,274,17,69,64,59,244,239,249,254,259,264,373,369,344,339,334,354,349,364,359,379,141,135,146,27,21,290,328,329,327,325,326,324,296,166,170,160,150,155,92,87,277,83,73,77,97,102,107,6,7,282,181,186,176,195,200,190,121,110,115,131,126,285,230,220,225,216,205,211,45,266,50,30,36,41,8,270,9,66,60,56,242,237,246,251,256,261,370,366,340,336,330,352,347,360,355,375,142,137,147,28,22,292,302,301,300,305,303,304,297,167,172,162,152,157,90,86,275,82,70,75,96,101,106,2,3,280,183,188,178,198,203,193,122,112,117,132,127,287,233,223,228,218,208,213,48,268,53,33,38,42,14,273,15,68,63,58,240,235,248,253,258,263,372,367,343,338,333,350,345,362,357,377 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#a7c342f115ba9e95260599f60b9f7eeb7d0c7792c4f4de7d123ccd3c5ebc1a9f, M = {67} 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 23:39:23 · history