Equation 677 Database

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Magma 68f03a508bc3…

magma 68f03a508bc3
Size
381
Isomorphism class hash
68f03a508bc3f403c0ef5edbc5ca333925aece111453f690ba0258a7029441a4
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 23:38:14
Display reorder
380,192,102,94,157,109,322,116,101,227,262,242,202,104,90,167,111,318,118,97,237,207,247,105,91,172,112,319,119,98,212,106,252,182,92,177,113,320,114,99,217,265,271,276,281,286,292,197,103,95,162,110,317,117,96,232,107,257,187,93,152,108,321,115,100,222,296,375,346,348,347,361,349,345,366,356,372,190,35,50,155,36,311,43,57,225,260,240,200,31,52,166,38,313,45,59,235,205,245,32,53,171,39,314,46,54,211,33,250,181,48,176,40,315,47,55,216,267,272,277,282,287,290,195,30,51,161,37,312,44,58,230,34,256,186,49,150,41,316,42,56,220,297,377,339,336,335,362,337,338,365,355,370,191,19,11,156,26,305,4,12,226,261,241,201,21,7,165,28,307,1,14,236,206,246,22,8,170,29,308,0,15,210,23,251,180,9,175,24,309,2,16,215,266,270,275,280,285,291,196,20,6,160,27,306,5,13,231,18,255,185,10,151,25,310,3,17,221,295,376,332,334,333,360,330,331,369,359,371,194,129,144,159,136,304,143,122,229,264,244,204,131,146,169,132,300,139,124,239,209,249,126,147,174,133,329,140,125,214,127,254,184,148,179,134,302,141,120,219,269,274,279,284,289,294,199,130,145,164,137,301,138,123,234,128,259,189,149,154,135,303,142,121,224,299,378,350,352,351,363,353,354,368,357,374,193,67,88,158,74,328,81,60,228,263,243,203,69,84,168,76,324,83,62,238,208,248,70,85,173,77,325,78,63,213,71,253,183,86,178,72,326,79,64,218,268,273,278,283,288,293,198,68,89,163,75,323,82,61,233,66,258,188,87,153,73,327,80,65,223,298,379,340,342,341,364,343,344,367,358,373 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#a5ceaca916191ef68f2e3b6b2367dcc497ee860690a383f5692cc65c6f41ad3d, 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 23:38:15 · history