Equation 677 Database

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Magma 030cd42432ce…

magma 030cd42432ce
Size
381
Isomorphism class hash
030cd42432ce050c8950d522ebd9b048da7b7460c4a5bfdb25096f83b13f4b34
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 23:38:34
Display reorder
380,326,325,324,328,329,327,167,171,160,180,185,175,206,286,212,191,196,200,236,240,231,220,225,216,98,103,93,298,88,83,108,113,118,123,128,133,283,138,143,148,153,158,7,12,2,293,23,19,45,51,41,31,37,28,256,245,252,271,262,266,278,73,78,55,61,66,343,348,335,330,363,350,358,378,372,365,312,314,313,317,315,316,169,173,164,182,187,178,208,288,213,192,198,203,238,243,233,223,228,217,97,102,92,297,87,82,107,112,117,122,127,132,282,137,142,147,152,157,8,13,3,292,21,16,47,52,42,30,35,25,258,248,253,273,263,268,277,72,77,59,64,69,342,347,337,332,362,352,357,377,370,367,303,305,304,302,301,300,168,172,163,183,188,176,207,285,210,193,197,202,237,242,232,222,227,218,95,100,90,295,86,81,106,111,115,121,126,131,280,135,140,145,150,155,5,10,0,291,22,17,49,53,44,32,39,27,255,246,250,270,260,265,276,70,75,58,63,68,341,345,338,333,360,353,356,376,371,368,320,319,318,322,323,321,165,170,162,181,186,177,205,287,211,190,195,201,235,241,230,221,226,215,96,101,91,296,85,80,105,110,116,120,125,130,281,136,141,146,151,156,6,11,1,290,20,15,48,54,43,33,38,26,257,247,251,272,261,267,275,71,76,56,60,65,340,346,336,331,361,351,355,375,374,366,307,306,308,309,310,311,166,174,161,184,189,179,209,289,214,194,199,204,239,244,234,224,229,219,99,104,94,299,89,84,109,114,119,124,129,134,284,139,144,149,154,159,9,14,4,294,24,18,46,50,40,34,36,29,259,249,254,274,264,269,279,74,79,57,62,67,344,349,339,334,364,354,359,379,373,369 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#a6a871b690da3ca50898b154241f95e49e76adc5851f18be5057763f1765447f, 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 23:38:35 · history