Equation 677 Database

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Magma 394fe5f74e21…

magma 394fe5f74e21
Size
381
Isomorphism class hash
394fe5f74e212610d53c445ff0c9fe954024b398eb2e2ab8daad2f7916d228a3
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 23:44:08
Display reorder
380,221,203,184,216,239,324,191,211,232,198,237,201,219,185,217,325,189,212,233,199,220,202,183,218,238,323,190,210,231,200,213,327,186,230,236,195,226,208,194,224,214,328,187,228,222,234,196,227,209,192,215,326,188,229,223,235,197,225,207,193,206,204,182,180,181,205,338,340,356,364,354,355,330,373,374,339,69,103,115,95,108,315,90,62,80,73,109,104,70,116,93,316,91,60,78,74,71,102,114,94,110,314,92,61,79,72,65,312,87,105,83,98,75,119,66,100,63,313,88,106,101,81,96,76,117,67,64,311,89,107,99,82,97,77,118,68,85,86,112,113,111,84,371,362,351,335,336,352,337,334,363,372,139,146,128,135,121,305,164,159,177,172,122,144,140,126,136,306,162,160,178,173,138,145,127,137,120,307,163,161,179,171,132,308,131,149,151,169,174,156,167,141,133,309,129,147,142,152,170,175,157,165,134,310,130,148,143,150,168,176,158,166,123,124,153,154,155,125,379,333,349,369,361,378,350,360,370,353,291,241,265,284,255,304,280,271,251,299,256,240,292,266,282,329,281,272,249,297,293,242,264,283,257,303,279,270,250,298,277,300,274,248,253,290,245,269,285,294,278,302,275,246,295,254,288,243,267,286,276,301,273,247,296,252,289,244,268,287,259,260,262,263,261,258,342,367,343,366,331,365,341,357,375,332,43,48,30,22,18,319,2,35,53,29,19,49,44,31,23,317,1,33,51,27,42,50,32,21,20,318,0,34,52,28,38,322,10,15,56,24,14,8,40,45,36,320,11,16,46,54,25,12,6,41,37,321,9,17,47,55,26,13,7,39,58,59,4,5,3,57,377,344,347,346,358,359,376,348,345,368 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#d2a61d29742d49dd19922ccc12aa75e870a46faf3bc859fdd0d579ff1b31399f, 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 23:44:09 · history