Equation 677 Database

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Magma 4c29a4a6d039…

magma 4c29a4a6d039
Size
381
Isomorphism class hash
4c29a4a6d039d71714e1211011c08f83c32c70bf14116a6a4b0d9448c0decf0d
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 23:41:11
Display reorder
380,106,105,107,102,103,104,88,89,84,85,86,87,278,282,288,293,298,273,258,263,268,243,248,253,99,100,101,96,97,98,90,91,92,93,94,95,129,130,131,126,127,128,202,236,198,199,200,201,328,323,324,325,326,327,197,192,193,194,195,196,122,124,125,121,120,123,348,347,349,352,346,330,364,372,378,363,213,212,214,209,210,211,170,171,172,173,168,169,275,284,286,291,296,270,256,261,266,240,246,251,206,207,208,203,204,205,179,174,175,176,177,178,8,9,10,11,6,7,132,133,134,135,136,137,311,306,307,308,309,310,141,142,143,138,139,140,2,4,5,237,0,3,331,361,365,333,360,334,353,371,376,354,22,21,23,18,19,20,30,31,32,33,34,35,277,280,285,292,297,272,255,260,265,241,245,250,15,16,17,12,13,14,29,24,25,26,27,28,164,165,166,167,162,163,215,216,217,218,219,238,329,322,319,320,321,318,223,224,225,220,221,222,156,158,159,161,160,157,332,336,335,359,337,358,366,374,375,367,190,189,191,186,187,188,66,67,68,69,70,71,276,281,287,290,295,271,257,262,267,242,247,252,183,184,185,180,181,182,65,60,61,62,63,64,229,230,231,226,227,228,38,39,40,41,36,37,317,312,313,314,315,316,44,45,46,47,42,43,1,234,235,233,232,239,355,342,362,368,343,369,338,370,377,339,149,148,144,145,146,147,75,76,77,72,73,74,279,283,289,294,299,274,259,264,269,244,249,254,154,155,150,151,152,153,82,83,78,79,80,81,118,119,114,115,116,117,56,57,58,59,54,55,301,300,302,303,304,305,50,51,52,53,48,49,113,109,110,112,111,108,357,344,356,351,345,350,341,373,379,340 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#b66edbbdcc18ab822aeb8c0e517cc0500614bfcd68d760a94b6b8cc01b086dc5, 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 23:41:12 · history