Equation 677 Database

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Magma e60536fb4441…

magma e60536fb4441
Size
381
Isomorphism class hash
e60536fb44410c0acfbba010ad4f108c4d893f7d34b3e94d2d53ea36c416833f
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 23:27:40
Display reorder
380,304,303,305,301,300,302,152,155,160,167,297,172,281,100,106,96,86,91,115,120,110,285,130,126,206,211,215,221,226,231,245,237,241,260,250,255,25,266,30,10,15,24,56,51,270,36,41,45,2,290,3,145,136,141,186,175,181,190,200,195,75,70,80,61,275,66,360,336,340,365,355,330,351,345,371,375,307,306,308,309,310,311,150,157,161,165,296,171,280,101,105,95,85,90,116,121,111,286,131,125,207,212,217,222,227,232,248,235,240,263,253,258,27,267,32,12,17,20,57,52,272,37,42,47,1,291,0,146,135,140,187,177,182,192,202,197,76,71,81,60,276,65,361,337,342,366,356,333,350,346,372,377,316,315,317,312,313,314,154,159,164,169,299,174,284,104,109,99,89,94,119,124,114,289,134,129,209,214,219,224,229,234,249,239,244,264,254,259,29,269,34,14,19,23,59,54,274,39,44,49,8,294,9,149,139,144,189,179,184,194,204,199,79,74,84,64,279,69,364,339,344,368,359,334,354,349,374,379,320,319,318,322,323,321,153,158,163,168,298,173,283,103,108,98,88,93,118,123,113,288,133,128,208,213,218,223,228,233,246,236,242,261,251,256,28,268,33,13,18,21,58,53,273,38,43,48,6,293,7,148,138,143,188,178,183,193,203,198,78,73,83,63,278,68,363,338,343,367,358,331,353,348,373,378,329,328,327,325,326,324,151,156,162,166,295,170,282,102,107,97,87,92,117,122,112,287,132,127,205,210,216,220,225,230,247,238,243,262,252,257,26,265,31,11,16,22,55,50,271,35,40,46,4,292,5,147,137,142,185,176,180,191,201,196,77,72,82,62,277,67,362,335,341,369,357,332,352,347,370,376 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#564914c332df918b1bab25ab6758cc0c591864f3f64c8c0ef251305010e22f83, M = {76} 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 23:27:41 · history