Equation 677 Database

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Magma 2fed311e7be4…

magma 2fed311e7be4
Size
381
Isomorphism class hash
2fed311e7be4f987508b473e7e68bf0579b4aca85c8f370348d021f706599378
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 23:22:26
Display reorder
380,319,323,321,31,50,11,156,176,136,131,151,170,101,61,71,81,201,221,181,115,75,85,106,206,225,186,36,56,15,236,231,255,260,261,275,271,246,318,322,41,1,146,126,161,121,91,191,281,65,196,216,26,46,241,251,320,21,165,141,110,211,95,286,6,295,290,377,330,357,347,341,338,351,371,364,368,308,306,310,34,54,14,159,179,139,133,154,173,104,63,73,84,204,224,183,119,79,88,109,208,229,189,39,58,18,239,233,258,269,267,279,274,248,307,311,44,4,148,129,164,123,94,193,283,69,199,219,29,49,244,254,309,23,169,144,113,214,99,289,8,299,294,378,333,358,348,343,335,353,373,363,367,305,303,300,30,51,10,155,175,135,130,150,171,100,60,70,80,200,220,180,116,76,86,105,205,226,185,35,55,16,235,230,256,263,262,276,270,245,304,302,40,0,145,125,160,120,90,190,280,66,195,215,25,45,240,250,301,20,166,140,111,210,96,285,5,296,291,376,332,356,346,340,339,350,370,366,362,312,316,314,33,53,13,158,178,138,134,153,174,103,64,74,83,203,223,184,118,78,89,108,209,228,188,38,59,19,238,234,259,268,266,278,273,249,317,315,43,3,149,128,163,124,93,194,284,68,198,218,28,48,243,253,313,24,168,143,114,213,98,288,9,298,293,379,334,359,349,344,337,354,374,369,361,327,325,329,32,52,12,157,177,137,132,152,172,102,62,72,82,202,222,182,117,77,87,107,207,227,187,37,57,17,237,232,257,265,264,277,272,247,326,324,42,2,147,127,162,122,92,192,282,67,197,217,27,47,242,252,328,22,167,142,112,212,97,287,7,297,292,375,331,355,345,342,336,352,372,360,365 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#4422b92082c5ba9f603861f57ee03bc11c9f901f0082cee83e1cd8bfe00bbd4d, M = {74} 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 23:22:28 · history