Equation 677 Database

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Magma 75bc1581862c…

magma 75bc1581862c
Size
381
Isomorphism class hash
75bc1581862c8f4201b10cdb220e6a3b852610e962aebbe90f3ec879b288686f
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 23:45:25
Display reorder
380,326,325,324,328,329,327,63,68,58,243,53,48,16,17,18,19,214,274,144,149,139,129,134,124,209,199,204,194,184,189,154,159,164,169,174,179,239,289,234,224,229,219,113,118,293,98,103,108,299,23,28,33,38,43,78,82,73,283,93,88,248,258,253,278,263,268,353,338,334,368,358,343,374,349,364,378,319,318,320,321,322,323,62,67,57,242,52,47,12,15,13,14,213,273,143,148,138,128,133,123,208,198,203,193,183,188,153,158,163,168,173,178,238,288,233,223,228,218,112,117,292,97,102,107,297,22,27,32,37,42,77,81,72,282,92,87,245,255,250,277,262,267,352,337,333,367,357,342,373,348,363,377,316,315,317,312,313,314,60,66,55,240,51,46,0,2,3,1,212,270,140,145,135,126,131,121,206,196,201,190,180,185,151,156,161,165,170,176,237,287,232,222,227,217,110,115,291,95,101,106,295,21,26,31,35,40,75,84,71,281,90,85,246,257,251,276,261,266,351,336,331,366,355,341,370,347,361,375,306,308,307,311,309,310,64,69,59,244,54,49,9,10,8,4,211,272,142,147,137,127,132,122,207,197,202,192,182,187,152,157,162,167,172,177,236,286,231,220,225,215,114,119,294,99,104,109,298,24,29,34,39,44,79,83,74,284,94,89,249,259,254,279,264,269,354,335,332,369,359,344,372,346,362,379,305,304,303,300,302,301,61,65,56,241,50,45,7,5,6,11,210,271,141,146,136,125,130,120,205,195,200,191,181,186,150,155,160,166,171,175,235,285,230,221,226,216,111,116,290,96,100,105,296,20,25,30,36,41,76,80,70,280,91,86,247,256,252,275,260,265,350,339,330,365,356,340,371,345,360,376 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#dba6afe67f86b36e533f777300b41b8ae8b2a840d4529c92a6cd7ab996e48d4f, M = {69} 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 23:45:26 · history