Equation 677 Database

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Magma c27cffdbdee4…

magma c27cffdbdee4
Size
381
Isomorphism class hash
c27cffdbdee4efbf2597d252c8adb4c19302f6f6c5e811e7ed7b8092c70d563d
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 331 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:44:13
Display reorder
380,169,24,10,178,303,311,167,25,8,176,177,312,168,23,9,161,21,27,306,156,22,162,28,304,157,20,163,26,155,305,173,158,4,153,13,174,159,2,154,11,175,160,3,152,12,164,5,16,151,170,165,6,14,150,171,166,7,15,298,172,17,18,1,0,149,19,373,350,354,377,372,346,355,345,374,347,207,47,35,201,302,318,208,48,36,202,200,301,206,49,37,186,32,50,310,192,33,187,51,319,193,34,185,52,191,300,184,190,42,196,54,182,188,43,194,55,183,189,41,195,53,205,39,57,199,181,203,40,58,197,179,204,38,56,198,180,31,29,45,46,44,30,379,349,348,376,356,352,375,353,378,351,242,112,100,266,323,308,243,113,101,267,265,321,241,114,102,251,97,115,307,257,98,252,116,327,258,99,250,117,256,320,249,255,107,261,89,247,253,108,259,90,248,254,106,260,88,240,104,92,264,246,238,105,93,262,244,239,103,91,263,245,96,94,110,111,109,95,365,336,335,363,364,338,362,337,366,339,215,85,76,209,313,325,216,86,74,210,211,324,217,87,75,224,73,61,328,230,71,225,59,322,231,72,226,60,232,309,222,228,80,234,62,223,229,81,235,63,221,227,82,233,64,213,77,65,237,219,214,78,66,236,220,212,79,67,299,218,69,70,83,84,148,68,370,341,340,368,369,343,367,342,371,344,288,127,130,278,314,315,286,128,131,279,277,316,287,129,132,272,121,133,317,290,122,273,135,326,291,123,271,134,289,329,270,285,146,297,137,268,283,147,295,138,269,284,145,296,136,281,140,142,276,294,282,141,143,274,292,280,139,144,275,293,120,118,125,126,124,119,361,332,330,359,360,334,358,333,357,331 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#d4908b869d5ae67b274ea23e98d3a2b2496095883ef30e4d122d513034ccac45, 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 23:44:14 · history