Equation 677 Database

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Magma f085929a07d7…

magma f085929a07d7
Size
381
Isomorphism class hash
f085929a07d7f0c7bcf0b507e04f3741e38a43dd83f68644beac8c95a81b3ace
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 23:36:34
Display reorder
380,115,125,120,111,106,27,25,26,30,28,29,101,17,18,16,251,41,19,75,80,89,91,290,96,265,256,260,285,271,275,131,136,141,145,150,155,200,191,196,216,206,211,241,246,296,225,230,235,221,43,42,45,280,44,175,180,185,161,166,171,303,304,305,301,300,302,346,360,350,331,340,356,370,365,336,376,116,126,121,110,105,22,20,21,35,23,24,100,38,36,37,250,39,40,76,81,85,90,291,95,266,255,261,286,270,276,130,135,140,146,151,156,201,190,195,215,205,210,240,245,295,226,231,236,220,31,32,33,281,34,176,181,186,160,165,170,325,326,324,328,329,327,345,361,351,330,341,355,371,366,335,375,118,128,123,113,108,47,48,46,50,51,49,103,53,54,52,252,56,55,78,83,87,93,293,98,267,257,262,287,272,277,133,138,143,148,153,158,203,193,198,218,208,213,243,248,298,228,233,238,223,62,61,64,283,63,178,183,188,163,168,173,317,315,316,314,312,313,347,363,353,333,343,357,373,367,338,377,117,127,122,112,107,9,7,8,12,10,11,102,15,13,14,253,6,5,77,82,86,92,292,97,268,258,263,288,273,278,132,137,142,147,152,157,202,192,197,217,207,212,242,247,297,227,232,237,222,58,57,60,282,59,177,182,187,162,167,172,319,320,318,322,323,321,349,362,352,332,342,358,372,368,337,378,119,129,124,114,109,0,69,1,4,2,3,104,73,74,72,254,71,70,79,84,88,94,294,99,269,259,264,289,274,279,134,139,144,149,154,159,204,194,199,219,209,214,244,249,299,229,234,239,224,66,65,68,284,67,179,184,189,164,169,174,306,307,308,309,310,311,348,364,354,334,344,359,374,369,339,379 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#9acf37934a26f07a9500b1ccb24642817fa617552582595ca38f94c8a1f3c019, 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 23:36:35 · history