Equation 677 Database

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Magma 7ce14498e0f1…

magma 7ce14498e0f1
Size
381
Isomorphism class hash
7ce14498e0f15ba31f1de7345236f709a1b358cc3fd1019241def377b6289e72
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 23:50:03
Display reorder
380,311,310,309,307,308,306,180,185,175,196,200,191,83,88,78,98,283,93,116,285,120,103,107,113,206,211,216,220,225,230,145,140,291,136,126,131,273,28,33,38,43,48,63,53,58,73,68,278,22,16,267,11,0,9,259,250,260,236,241,245,160,171,165,155,296,150,370,334,353,366,355,343,361,338,348,376,321,320,322,317,318,319,184,189,179,199,204,194,84,89,79,99,284,94,115,286,121,100,106,111,209,214,219,224,229,234,149,144,294,139,129,134,274,29,34,39,44,49,64,54,59,74,69,279,23,18,268,12,2,6,256,253,263,238,243,248,164,174,169,159,299,154,374,331,354,368,356,344,364,339,349,379,328,327,326,324,325,323,181,186,176,195,201,190,82,87,77,97,282,92,117,287,122,102,108,112,205,210,215,221,226,231,146,141,290,135,125,130,272,27,32,37,42,47,62,52,57,72,67,277,20,17,266,10,1,8,258,252,262,235,240,246,161,170,166,156,295,151,371,333,352,365,357,342,360,337,347,375,314,316,315,329,312,313,183,188,178,198,203,193,81,86,76,95,280,90,119,289,124,104,109,114,208,213,218,223,228,233,148,143,293,138,128,133,271,25,30,36,41,46,60,50,55,70,66,275,24,19,269,14,4,7,257,254,264,239,244,249,163,173,168,158,298,153,373,332,350,367,359,341,363,336,345,378,303,305,304,302,301,300,182,187,177,197,202,192,80,85,75,96,281,91,118,288,123,101,105,110,207,212,217,222,227,232,147,142,292,137,127,132,270,26,31,35,40,45,61,51,56,71,65,276,21,15,265,13,3,5,255,251,261,237,242,247,162,172,167,157,297,152,372,330,351,369,358,340,362,335,346,377 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#edf00a573dad398077d9e9a7f74ac5f2ae5601c41b127cdfd29539dca9f6b98a, M = {75} 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 23:50:04 · history