Equation 677 Database

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Magma 50420be5873d…

magma 50420be5873d
Size
381
Isomorphism class hash
50420be5873d2ca2cda6b11aed07a5af3f4ce087af73c91aab82c226e831d845
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 23:44:04
Display reorder
380,272,248,253,295,288,326,268,279,259,287,247,270,252,296,289,323,269,280,260,285,271,246,256,294,290,324,267,281,258,286,265,321,276,262,273,249,254,298,293,283,266,316,277,263,284,274,250,255,299,291,264,318,278,261,282,275,251,257,297,292,241,240,243,244,245,242,339,338,354,365,353,352,332,373,372,337,19,26,57,14,9,317,34,39,62,44,24,20,58,12,10,319,35,40,60,42,18,25,59,13,11,320,33,41,61,43,65,322,21,31,36,54,29,49,47,6,63,325,22,32,7,37,55,27,50,45,64,327,23,30,8,38,56,28,48,46,17,15,51,52,53,16,375,366,356,342,340,355,341,343,367,374,139,146,177,133,129,303,154,159,182,164,144,140,178,134,130,304,155,160,180,162,138,145,179,132,131,302,153,161,181,163,136,301,141,151,156,174,149,169,167,126,137,310,142,152,127,157,175,147,170,165,135,300,143,150,128,158,176,148,168,166,1,0,171,172,173,2,379,333,350,370,361,378,349,359,369,360,233,189,222,214,209,311,230,204,202,195,190,234,223,212,210,312,231,205,200,196,235,188,221,213,211,313,232,203,201,194,229,329,192,224,237,219,5,239,197,206,227,314,193,225,207,238,220,3,183,198,228,315,191,226,208,236,218,4,184,199,217,215,187,185,186,216,336,363,335,362,330,364,334,351,371,331,98,116,78,88,106,306,124,71,82,67,114,96,79,89,107,307,125,69,83,68,97,115,80,87,105,305,123,70,81,66,91,309,101,121,95,75,119,108,85,103,92,328,99,122,104,93,76,117,109,86,90,308,100,120,102,94,77,118,110,84,74,72,113,111,112,73,377,346,347,348,358,357,376,345,344,368 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#d08bad00a7853889faa2a48338611ef91bafb3bf67fae9d85c6f3c5fac5bd4d3, 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 23:44:05 · history