Equation 677 Database

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Magma 78f24d1151e3…

magma 78f24d1151e3
Size
381
Isomorphism class hash
78f24d1151e3c2d1d5c2e94256b39feddcf00ba44ddeecb509b425021064f9f2
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 23:24:54
Display reorder
380,211,235,216,221,226,231,110,116,90,95,100,105,145,121,126,131,135,140,170,175,151,156,160,165,191,196,200,205,181,186,35,41,46,51,56,30,256,261,266,240,246,251,325,326,327,328,329,324,71,76,80,85,61,66,11,21,6,26,0,16,286,295,281,271,276,291,337,353,370,368,330,336,351,350,342,377,214,238,219,224,229,233,113,118,94,99,103,108,148,124,129,134,139,144,173,178,154,158,163,168,193,198,203,208,184,189,38,43,49,54,58,33,259,263,268,244,249,254,309,310,311,306,307,308,73,78,83,88,64,68,14,23,9,29,4,18,288,298,284,274,279,293,343,359,372,366,362,348,341,363,360,378,210,236,215,220,225,230,111,115,91,96,101,106,146,120,125,130,136,141,171,176,150,155,161,166,190,195,201,206,180,185,36,40,45,50,55,31,255,260,265,241,245,250,323,318,319,320,321,322,70,75,81,86,60,65,10,20,5,25,1,15,285,296,280,270,275,292,346,355,371,369,333,335,347,354,332,375,213,239,218,223,228,234,114,119,93,98,104,109,149,123,128,133,138,143,174,179,153,159,164,169,194,199,204,209,183,188,39,44,48,53,59,34,258,264,269,243,248,253,312,313,314,315,316,317,74,79,84,89,63,69,13,24,8,28,3,19,289,299,283,273,278,294,331,349,374,365,361,358,344,364,339,376,212,237,217,222,227,232,112,117,92,97,102,107,147,122,127,132,137,142,172,177,152,157,162,167,192,197,202,207,182,187,37,42,47,52,57,32,257,262,267,242,247,252,301,300,302,303,304,305,72,77,82,87,62,67,12,22,7,27,2,17,287,297,282,272,277,290,340,338,373,367,334,352,357,356,345,379 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#4ff69c35f55aa106c20b4528e074e3f72eddedd150e00069ea529e91bc9e2010, 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 23:24:55 · history