Equation 677 Database

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Magma f3b13cf4d952…

magma f3b13cf4d952
Size
381
Isomorphism class hash
f3b13cf4d952a8f93cfa81d6f96977a154bdf3f2e9eecbdfde2b3786de9253d2
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 23:35:44
Display reorder
380,307,306,308,309,310,311,195,200,190,181,186,176,45,36,41,30,25,271,280,96,91,81,86,76,2,7,12,19,265,23,216,206,211,230,220,228,100,105,110,116,121,286,237,241,246,250,256,261,70,65,276,60,51,55,165,170,161,151,156,295,292,146,142,130,136,125,365,341,345,350,332,356,360,372,335,375,317,316,315,313,314,312,198,203,193,183,188,178,46,35,40,31,26,270,281,95,90,80,85,75,3,6,13,15,266,22,217,208,212,232,222,225,101,106,111,115,120,285,235,244,249,251,255,260,71,66,275,61,50,56,167,172,162,152,157,297,290,145,140,132,137,127,367,340,346,351,330,355,362,371,336,378,322,321,323,318,319,320,196,201,191,180,185,175,48,38,43,33,28,273,283,98,93,83,88,78,1,5,10,17,268,20,215,205,210,231,221,226,103,108,113,118,123,288,236,243,247,253,258,263,73,68,278,63,53,58,166,171,160,150,155,296,291,147,141,131,135,126,366,343,348,353,331,357,361,370,338,376,301,302,300,305,303,304,197,202,192,182,187,177,47,37,42,32,27,272,282,97,92,82,87,77,0,8,11,16,267,21,218,207,213,233,223,227,102,107,112,117,122,287,238,242,248,252,257,262,72,67,277,62,52,57,168,173,163,153,158,298,293,148,143,133,138,128,368,342,347,352,333,359,363,373,337,377,326,325,324,328,329,327,199,204,194,184,189,179,49,39,44,34,29,274,284,99,94,84,89,79,4,9,14,18,269,24,219,209,214,234,224,229,104,109,114,119,124,289,239,240,245,254,259,264,74,69,279,64,54,59,169,174,164,154,159,299,294,149,144,134,139,129,369,344,349,354,334,358,364,374,339,379 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#8e237b368ce49904371f47a0bbc192c3f49c4a8da81336b4c06fd9fdc3a5d75d, M = {68} 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 23:35:45 · history