Equation 677 Database

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Magma bca95bb265f1…

magma bca95bb265f1
Size
381
Isomorphism class hash
bca95bb265f148ddffdda4be2176d2e03ad4eff75ce113534987d8c86cc35624
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 23:34:41
Display reorder
380,88,98,93,108,103,298,78,83,73,63,68,58,133,138,128,118,123,168,158,163,153,143,148,43,48,53,28,33,38,266,271,264,280,286,209,214,204,224,229,219,293,23,17,8,13,178,183,173,193,198,188,244,234,239,259,249,254,304,305,303,300,302,275,113,3,301,368,374,338,344,333,353,348,359,363,378,85,95,90,107,101,297,75,80,70,61,66,56,130,135,125,115,120,165,156,160,150,141,146,40,45,50,26,31,36,265,270,260,281,285,206,211,200,220,226,215,290,20,18,6,10,175,180,170,191,196,186,241,230,237,255,246,251,306,329,307,308,309,276,112,0,310,367,370,335,340,330,352,346,355,360,375,89,99,94,109,104,299,79,84,74,64,69,59,134,139,129,119,124,169,159,164,154,144,149,44,49,54,29,34,39,269,274,263,284,289,208,213,203,223,228,218,294,24,15,9,14,179,184,174,194,199,189,243,233,238,258,248,253,314,315,316,311,312,279,114,4,313,369,373,339,343,334,354,349,358,364,379,86,96,91,105,100,295,76,81,71,60,65,55,131,137,127,117,121,167,157,162,152,142,147,41,46,51,25,30,35,267,272,261,282,287,205,210,201,221,225,216,291,21,16,5,11,176,181,171,190,195,185,242,232,236,256,245,250,328,326,327,325,323,277,111,1,324,365,371,336,341,331,350,345,356,361,376,87,97,92,106,102,296,77,82,72,62,67,57,132,136,126,116,122,166,155,161,151,140,145,42,47,52,27,32,37,268,273,262,283,288,207,212,202,222,227,217,292,22,19,7,12,177,182,172,192,197,187,240,231,235,257,247,252,318,319,317,321,322,278,110,2,320,366,372,337,342,332,351,347,357,362,377 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#890900158510c31f70f4fa8bc84bbffcea5cd35bea72b3996f708723e8ad424c, M = {70} 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 23:34:42 · history