Equation 677 Database

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Magma d74ee956fc59…

magma d74ee956fc59
Size
381
Isomorphism class hash
d74ee956fc5968770c6a87b431ced430ae3f8fc8a5470342408ca3ff62849289
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 23:49:55
Display reorder
380,90,95,281,85,76,81,180,185,176,195,200,190,290,126,131,145,137,141,20,10,15,265,0,5,241,246,235,256,261,251,117,120,286,100,106,112,206,211,216,220,225,230,295,170,166,155,160,150,308,306,307,311,309,310,71,66,275,50,55,60,26,36,31,46,40,271,331,345,360,341,335,370,357,365,352,375,92,96,282,86,75,80,181,187,177,197,201,191,292,127,132,147,135,140,21,11,16,266,2,6,240,245,236,255,260,250,116,122,287,102,108,113,205,210,215,221,226,231,297,172,167,157,162,152,319,320,318,322,323,321,72,67,277,52,57,62,27,37,32,47,42,272,330,347,362,342,336,371,356,367,351,379,91,99,280,87,77,82,182,186,175,196,202,192,291,125,130,146,136,142,22,12,17,267,1,9,242,247,237,257,262,252,115,121,285,101,107,110,207,212,217,222,227,232,296,171,165,156,161,151,301,300,302,303,304,305,70,65,276,51,56,61,25,35,30,45,41,270,332,346,361,340,337,372,355,366,350,376,94,98,284,89,79,84,183,188,178,198,203,193,293,128,133,148,139,144,23,13,18,268,3,7,243,248,238,258,263,253,119,124,289,104,109,114,208,213,218,223,228,233,298,173,168,158,163,153,326,324,325,329,327,328,73,68,278,53,58,63,28,38,33,48,43,273,333,348,363,343,338,373,359,368,354,377,93,97,283,88,78,83,184,189,179,199,204,194,294,129,134,149,138,143,24,14,19,269,4,8,244,249,239,259,264,254,118,123,288,103,105,111,209,214,219,224,229,234,299,174,169,159,164,154,317,315,316,314,312,313,74,69,279,54,59,64,29,39,34,49,44,274,334,349,364,344,339,374,358,369,353,378 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#edf00a573dad398077d9e9a7f74ac5f2ae5601c41b127cdfd29539dca9f6b98a, M = {73} 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 23:49:56 · history